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#-*- coding:utf-8 -*-
from builtins import range
from functools import total_ordering
@total_ordering
class moduint(object):
def __init__(self, arg):
self.arg = int(arg) % self.__class__.limit
assert(self.arg >= 0 and self.arg < self.__class__.limit)
def __repr__(self):
return self.__class__.__name__ + '(' + hex(self.arg) + ')'
def __hash__(self):
return hash(self.arg)
@classmethod
def maxcast(cls, c2):
c2 = c2.__class__
if cls.size > c2.size:
return cls
else:
return c2
def __eq__(self, y):
if isinstance(y, moduint):
return self.arg == y.arg
return self.arg == y
def __ne__(self, y):
# required Python 2.7.14
return not self == y
def __lt__(self, y):
if isinstance(y, moduint):
return self.arg < y.arg
return self.arg < y
def __add__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg + y.arg)
else:
return self.__class__(self.arg + y)
def __and__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg & y.arg)
else:
return self.__class__(self.arg & y)
def __div__(self, y):
# Python: 8 / -7 == -2 (C-like: -1)
# int(float) trick cannot be used, due to information loss
# Examples:
#
# 42 / 10 => 4
# 42 % 10 => 2
#
# -42 / 10 => -4
# -42 % 10 => -2
#
# 42 / -10 => -4
# 42 % -10 => 2
#
# -42 / -10 => 4
# -42 % -10 => -2
den = int(y)
num = int(self)
result_sign = 1 if (den * num) >= 0 else -1
cls = self.__class__
if isinstance(y, moduint):
cls = self.maxcast(y)
return (abs(num) // abs(den)) * result_sign
def __floordiv__(self, y):
return self.__div__(y)
def __int__(self):
return int(self.arg)
def __long__(self):
return int(self.arg)
def __index__(self):
return int(self.arg)
def __invert__(self):
return self.__class__(~self.arg)
def __lshift__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg << y.arg)
else:
return self.__class__(self.arg << y)
def __mod__(self, y):
# See __div__ for implementation choice
cls = self.__class__
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg - y * (self // y))
def __mul__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg * y.arg)
else:
return self.__class__(self.arg * y)
def __neg__(self):
return self.__class__(-self.arg)
def __or__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg | y.arg)
else:
return self.__class__(self.arg | y)
def __radd__(self, y):
return self.__add__(y)
def __rand__(self, y):
return self.__and__(y)
def __rdiv__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(y.arg // self.arg)
else:
return self.__class__(y // self.arg)
def __rfloordiv__(self, y):
return self.__rdiv__(y)
def __rlshift__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(y.arg << self.arg)
else:
return self.__class__(y << self.arg)
def __rmod__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(y.arg % self.arg)
else:
return self.__class__(y % self.arg)
def __rmul__(self, y):
return self.__mul__(y)
def __ror__(self, y):
return self.__or__(y)
def __rrshift__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(y.arg >> self.arg)
else:
return self.__class__(y >> self.arg)
def __rshift__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg >> y.arg)
else:
return self.__class__(self.arg >> y)
def __rsub__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(y.arg - self.arg)
else:
return self.__class__(y - self.arg)
def __rxor__(self, y):
return self.__xor__(y)
def __sub__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg - y.arg)
else:
return self.__class__(self.arg - y)
def __xor__(self, y):
if isinstance(y, moduint):
cls = self.maxcast(y)
return cls(self.arg ^ y.arg)
else:
return self.__class__(self.arg ^ y)
def __hex__(self):
return hex(self.arg)
def __abs__(self):
return abs(self.arg)
def __rpow__(self, v):
return v ** self.arg
def __pow__(self, v):
return self.__class__(self.arg ** v)
class modint(moduint):
def __init__(self, arg):
if isinstance(arg, moduint):
arg = arg.arg
a = arg % self.__class__.limit
if a >= self.__class__.limit // 2:
a -= self.__class__.limit
self.arg = a
assert(
self.arg >= -self.__class__.limit // 2 and
self.arg < self.__class__.limit
)
def is_modint(a):
return isinstance(a, moduint)
mod_size2uint = {}
mod_size2int = {}
mod_uint2size = {}
mod_int2size = {}
def define_int(size):
"""Build the 'modint' instance corresponding to size @size"""
global mod_size2int, mod_int2size
name = 'int%d' % size
cls = type(name, (modint,), {"size": size, "limit": 1 << size})
globals()[name] = cls
mod_size2int[size] = cls
mod_int2size[cls] = size
return cls
def define_uint(size):
"""Build the 'moduint' instance corresponding to size @size"""
global mod_size2uint, mod_uint2size
name = 'uint%d' % size
cls = type(name, (moduint,), {"size": size, "limit": 1 << size})
globals()[name] = cls
mod_size2uint[size] = cls
mod_uint2size[cls] = size
return cls
def define_common_int():
"Define common int"
common_int = range(1, 257)
for i in common_int:
define_int(i)
for i in common_int:
define_uint(i)
define_common_int()
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