'''simple docstring'''

def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):
 if n == 0:
  return 1

 elif n % 2 == 1:
  return (binary_exponentiation(UpperCAmelCase		,     n - 1		,     UpperCAmelCase     ) * a) % mod

 else:
  lowercase__				:    Tuple  =					binary_exponentiation(UpperCAmelCase		,     n / 2		,     UpperCAmelCase     )
  return (b * b) % mod


# a prime number
__a: Optional[Any]          =   7_01

__a: str          =   10_00_00_00_00
__a: int          =   10

# using binary exponentiation function, O(log(p)):
print((a / b) % p == (a * binary_exponentiation(b, p - 2, p)) % p)





print((a / b) % p == (a * b ** (p - 2)) % p)


'''simple docstring'''

import unittest

from knapsack import knapsack as k



class 			UpperCAmelCase  (						unittest.TestCase					):





       '''simple docstring'''



       def _lowerCAmelCase(						self )  ->  Tuple:
        lowercase__				:    Optional[Any]  =					0
        lowercase__				:    Any  =					[0]
        lowercase__				:    List[Any]  =					[0]
        lowercase__				:    Optional[Any]  =					len(__lowerCAmelCase )
        self.assertEqual(k.knapsack(__lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase )	,   0 )

        lowercase__				:    List[str]  =					[60]
        lowercase__				:    List[str]  =					[10]
        lowercase__				:    List[str]  =					len(__lowerCAmelCase )
        self.assertEqual(k.knapsack(__lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase )	,   0 )

       def _lowerCAmelCase(						self )  ->  Optional[Any]:
        lowercase__				:    Optional[Any]  =					3
        lowercase__				:    List[Any]  =					[1, 2, 3]
        lowercase__				:    Union[str, Any]  =					[3, 2, 1]
        lowercase__				:    List[Any]  =					len(__lowerCAmelCase )
        self.assertEqual(k.knapsack(__lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase )	,   5 )


       def _lowerCAmelCase(						self )  ->  Optional[Any]:
        lowercase__				:    int  =					50
        lowercase__				:    Any  =					[60, 100, 120]
        lowercase__				:    int  =					[10, 20, 30]
        lowercase__				:    Optional[Any]  =					len(__lowerCAmelCase )
        self.assertEqual(k.knapsack(__lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase )	,   220 )


if __name__ == "__main__":
  unittest.main()

