12521252 SUSTech Online Judge
Problem 1252 --[Median I] Factorial Magic

1252: [Median I] Factorial Magic

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 1179  Solved: 238
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Description

Neko is a freshman at SUSTech and he is good at fractorial problems. He wants to challenge you to see if you can solve the following problem: Caculate the value of \(((n!)!)!(mod\space m)\).

Input

There is only one line contains two integers \(n,m,(0{\leq}n{\leq}10^9,1{\leq}m{\leq}10^9)\).

Output

Print the value of \(((n!)!)!(mod\space m)\).

Sample Input

1 2019

Sample Output

1

HINT


In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n: For example, The value of 0! is 1, according to the convention for an empty product.

Source

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