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@@ -0,0 +1,354 @@
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+# after v1.2.2, int is always 64-bit
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+PyLong_SHIFT = 60//2 - 1
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+
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+PyLong_BASE = 2 ** PyLong_SHIFT
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+PyLong_MASK = PyLong_BASE - 1
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+PyLong_DECIMAL_SHIFT = 4
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+PyLong_DECIMAL_BASE = 10 ** PyLong_DECIMAL_SHIFT
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+
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+##############################################################
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+
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+def ulong_fromint(x: int):
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+ # return a list of digits and sign
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+ if x == 0: return [0], 1
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+ sign = 1 if x > 0 else -1
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+ if sign < 0: x = -x
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+ res = []
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+ while x:
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+ res.append(x & PyLong_MASK)
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+ x >>= PyLong_SHIFT
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+ return res, sign
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+
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+def ulong_cmp(a: list, b: list) -> int:
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+ # return 1 if a>b, -1 if a<b, 0 if a==b
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+ if len(a) > len(b): return 1
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+ if len(a) < len(b): return -1
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+ for i in range(len(a)-1, -1, -1):
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+ if a[i] > b[i]: return 1
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+ if a[i] < b[i]: return -1
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+ return 0
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+
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+def ulong_pad_(a: list, size: int):
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+ # pad leading zeros to have `size` digits
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+ delta = size - len(a)
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+ if delta > 0:
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+ a.extend([0] * delta)
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+
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+def ulong_unpad_(a: list):
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+ # remove leading zeros
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+ while len(a)>1 and a[-1]==0:
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+ a.pop()
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+
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+def ulong_add(a: list, b: list) -> list:
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+ res = [0] * max(len(a), len(b))
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+ ulong_pad_(a, len(res))
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+ ulong_pad_(b, len(res))
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+ carry = 0
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+ for i in range(len(res)):
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+ carry += a[i] + b[i]
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+ res[i] = carry & PyLong_MASK
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+ carry >>= PyLong_SHIFT
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+ if carry > 0:
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+ res.append(carry)
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+ return res
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+
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+def ulong_inc_(a: list):
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+ a[0] += 1
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+ for i in range(len(a)):
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+ if a[i] < PyLong_BASE: break
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+ a[i] -= PyLong_BASE
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+ if i+1 == len(a):
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+ a.append(1)
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+ else:
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+ a[i+1] += 1
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+
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+
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+def ulong_sub(a: list, b: list) -> list:
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+ # a >= b
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+ res = []
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+ borrow = 0
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+ for i in range(len(b)):
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+ tmp = a[i] - b[i] - borrow
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+ if tmp < 0:
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+ tmp += PyLong_BASE
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+ borrow = 1
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+ else:
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+ borrow = 0
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+ res.append(tmp)
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+ for i in range(len(b), len(a)):
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+ tmp = a[i] - borrow
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+ if tmp < 0:
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+ tmp += PyLong_BASE
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+ borrow = 1
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+ else:
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+ borrow = 0
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+ res.append(tmp)
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+ ulong_unpad_(res)
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+ return res
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+
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+def ulong_divmodi(a: list, b: int):
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+ # b > 0
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+ res = []
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+ carry = 0
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+ for i in range(len(a)-1, -1, -1):
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+ carry <<= PyLong_SHIFT
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+ carry += a[i]
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+ res.append(carry // b)
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+ carry %= b
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+ res.reverse()
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+ ulong_unpad_(res)
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+ return res, carry
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+
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+
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+def ulong_divmod(a: list, b: list):
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+
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+ if ulong_cmp(a, b) < 0:
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+ return [0], a
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+
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+ if len(b) == 1:
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+ q, r = ulong_divmodi(a, b[0])
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+ r, _ = ulong_fromint(r)
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+ return q, r
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+
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+ max = (len(a) - len(b)) * PyLong_SHIFT + \
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+ (a[-1].bit_length() - b[-1].bit_length())
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+
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+ low = [0]
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+
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+ high = (max // PyLong_SHIFT) * [0] + \
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+ [(2**(max % PyLong_SHIFT)) & PyLong_MASK]
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+
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+ while ulong_cmp(low, high) < 0:
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+ ulong_inc_(high)
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+ mid, r = ulong_divmodi(ulong_add(low, high), 2)
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+ if ulong_cmp(a, ulong_mul(b, mid)) >= 0:
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+ low = mid
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+ else:
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+ high = ulong_sub(mid, [1])
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+
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+ q = [0] * (len(a) - len(b) + 1)
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+ while ulong_cmp(a, ulong_mul(b, low)) >= 0:
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+ q = ulong_add(q, low)
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+ a = ulong_sub(a, ulong_mul(b, low))
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+ ulong_unpad_(q)
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+ return q, a
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+
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+def ulong_floordivi(a: list, b: int):
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+ # b > 0
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+ return ulong_divmodi(a, b)[0]
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+
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+def ulong_muli(a: list, b: int):
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+ # b >= 0
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+ res = [0] * len(a)
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+ carry = 0
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+ for i in range(len(a)):
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+ carry += a[i] * b
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+ res[i] = carry & PyLong_MASK
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+ carry >>= PyLong_SHIFT
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+ if carry > 0:
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+ res.append(carry)
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+ return res
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+
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+def ulong_mul(a: list, b: list):
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+ N = len(a) + len(b)
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+ # use grade-school multiplication
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+ res = [0] * N
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+ for i in range(len(a)):
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+ carry = 0
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+ for j in range(len(b)):
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+ carry += res[i+j] + a[i] * b[j]
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+ res[i+j] = carry & PyLong_MASK
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+ carry >>= PyLong_SHIFT
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+ res[i+len(b)] = carry
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+ ulong_unpad_(res)
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+ return res
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+
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+def ulong_powi(a: list, b: int):
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+ # b >= 0
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+ if b == 0: return [1]
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+ res = [1]
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+ while b:
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+ if b & 1:
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+ res = ulong_mul(res, a)
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+ a = ulong_mul(a, a)
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+ b >>= 1
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+ return res
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+
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+def ulong_repr(x: list) -> str:
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+ res = []
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+ while len(x)>1 or x[0]>0: # non-zero
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+ x, r = ulong_divmodi(x, PyLong_DECIMAL_BASE)
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+ res.append(str(r).zfill(PyLong_DECIMAL_SHIFT))
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+ res.reverse()
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+ s = ''.join(res)
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+ if len(s) == 0: return '0'
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+ if len(s) > 1: s = s.lstrip('0')
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+ return s
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+
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+def ulong_fromstr(s: str):
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+ if s[-1] == 'L':
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+ s = s[:-1]
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+ res, base = [0], [1]
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+ if s[0] == '-':
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+ sign = -1
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+ s = s[1:]
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+ else:
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+ sign = 1
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+ s = s[::-1]
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+ for c in s:
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+ c = ord(c) - 48
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+ assert 0 <= c <= 9
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+ res = ulong_add(res, ulong_muli(base, c))
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+ base = ulong_muli(base, 10)
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+ return res, sign
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+
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+class long:
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+ def __init__(self, x):
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+ if type(x) is tuple:
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+ self.digits, self.sign = x
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+ elif type(x) is int:
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+ self.digits, self.sign = ulong_fromint(x)
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+ elif type(x) is float:
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+ self.digits, self.sign = ulong_fromint(int(x))
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+ elif type(x) is str:
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+ self.digits, self.sign = ulong_fromstr(x)
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+ elif type(x) is long:
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+ self.digits, self.sign = x.digits.copy(), x.sign
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+ else:
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+ raise TypeError('expected int or str')
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+
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+ def __len__(self):
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+ return len(self.digits)
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+
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+ def __add__(self, other):
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+ if type(other) is int:
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+ other = long(other)
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+ elif type(other) is not long:
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+ return NotImplemented
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+ if self.sign == other.sign:
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+ return long((ulong_add(self.digits, other.digits), self.sign))
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+ else:
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+ cmp = ulong_cmp(self.digits, other.digits)
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+ if cmp == 0:
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+ return long(0)
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+ if cmp > 0:
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+ return long((ulong_sub(self.digits, other.digits), self.sign))
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+ else:
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+ return long((ulong_sub(other.digits, self.digits), other.sign))
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+
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+ def __radd__(self, other):
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+ return self.__add__(other)
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+
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+ def __sub__(self, other):
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+ if type(other) is int:
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+ other = long(other)
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+ elif type(other) is not long:
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+ return NotImplemented
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+ if self.sign != other.sign:
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+ return long((ulong_add(self.digits, other.digits), self.sign))
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+ cmp = ulong_cmp(self.digits, other.digits)
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+ if cmp == 0:
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+ return long(0)
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+ if cmp > 0:
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+ return long((ulong_sub(self.digits, other.digits), self.sign))
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+ else:
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+ return long((ulong_sub(other.digits, self.digits), -other.sign))
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+
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+ def __rsub__(self, other):
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+ if type(other) is int:
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+ other = long(other)
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+ elif type(other) is not long:
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+ return NotImplemented
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+ return other.__sub__(self)
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+
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+ def __mul__(self, other):
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+ if type(other) is int:
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+ return long((
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+ ulong_muli(self.digits, abs(other)),
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+ self.sign * (1 if other >= 0 else -1)
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+ ))
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+ elif type(other) is long:
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+ return long((
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+ ulong_mul(self.digits, other.digits),
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+ self.sign * other.sign
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+ ))
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+ return NotImplemented
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+
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+ def __rmul__(self, other):
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+ return self.__mul__(other)
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+
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+ #######################################################
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+ def __divmod__(self, other):
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+ if type(other) is int:
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+ assert self.sign == 1 and other > 0
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+ q, r = ulong_divmodi(self.digits, other)
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+ return long((q, 1)), r
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+ if type(other) is long:
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+ assert self.sign == 1 and other.sign == 1
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+ q, r = ulong_divmod(self.digits, other.digits)
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+ assert len(other)>1 or other.digits[0]>0
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+ return long((q, 1)), long((r, 1))
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+ raise NotImplementedError
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+
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+ def __floordiv__(self, other):
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+ return self.__divmod__(other)[0]
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+
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+ def __mod__(self, other):
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+ return self.__divmod__(other)[1]
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+
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+ def __pow__(self, other: int):
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+ assert type(other) is int and other >= 0
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+ if self.sign == -1 and other & 1:
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+ sign = -1
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+ else:
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+ sign = 1
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+ return long((ulong_powi(self.digits, other), sign))
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+
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+ def __lshift__(self, other: int):
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+ assert type(other) is int and other >= 0
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+ x = self.digits.copy()
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+ q, r = divmod(other, PyLong_SHIFT)
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+ x = [0]*q + x
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+ for _ in range(r): x = ulong_muli(x, 2)
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+ return long((x, self.sign))
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+
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|
|
+ def __rshift__(self, other: int):
|
|
|
|
|
+ assert type(other) is int and other >= 0
|
|
|
|
|
+ x = self.digits.copy()
|
|
|
|
|
+ q, r = divmod(other, PyLong_SHIFT)
|
|
|
|
|
+ x = x[q:]
|
|
|
|
|
+ if not x: return long(0)
|
|
|
|
|
+ for _ in range(r): x = ulong_floordivi(x, 2)
|
|
|
|
|
+ return long((x, self.sign))
|
|
|
|
|
+
|
|
|
|
|
+ def __neg__(self):
|
|
|
|
|
+ return long((self.digits, -self.sign))
|
|
|
|
|
+
|
|
|
|
|
+ def __cmp__(self, other):
|
|
|
|
|
+ if type(other) is int:
|
|
|
|
|
+ other = long(other)
|
|
|
|
|
+ elif type(other) is not long:
|
|
|
|
|
+ return NotImplemented
|
|
|
|
|
+ if self.sign > other.sign:
|
|
|
|
|
+ return 1
|
|
|
|
|
+ elif self.sign < other.sign:
|
|
|
|
|
+ return -1
|
|
|
|
|
+ else:
|
|
|
|
|
+ return ulong_cmp(self.digits, other.digits)
|
|
|
|
|
+
|
|
|
|
|
+ def __eq__(self, other):
|
|
|
|
|
+ return self.__cmp__(other) == 0
|
|
|
|
|
+ def __ne__(self, other):
|
|
|
|
|
+ return self.__cmp__(other) != 0
|
|
|
|
|
+ def __lt__(self, other):
|
|
|
|
|
+ return self.__cmp__(other) < 0
|
|
|
|
|
+ def __le__(self, other):
|
|
|
|
|
+ return self.__cmp__(other) <= 0
|
|
|
|
|
+ def __gt__(self, other):
|
|
|
|
|
+ return self.__cmp__(other) > 0
|
|
|
|
|
+ def __ge__(self, other):
|
|
|
|
|
+ return self.__cmp__(other) >= 0
|
|
|
|
|
+
|
|
|
|
|
+ def __repr__(self):
|
|
|
|
|
+ prefix = '-' if self.sign < 0 else ''
|
|
|
|
|
+ return prefix + ulong_repr(self.digits) + 'L'
|