GCC

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

The GNU Compiler Collection (usually shortened to GCC) is a compiler system produced by the GNU Project supporting various programming languages.  But it doesn’t contains the math operator “!”.

In mathematics the symbol represents the factorial operation. The expression n! means "the product of the integers from 1 to n". For example, 4! (read four factorial) is 4 × 3 × 2 × 1 = 24. (0! is defined as 1, which is a neutral element in multiplication, not multiplied by anything.)

We want you to help us with this formation: (0! + 1! + 2! + 3! + 4! + ... + n!)%m. 

Input

The first line consists of an integer T, indicating the number of test cases.

Each test on a single consists of two integer n and m. 

0 < T <= 20
0 <= n < 10100 (without leading zero)
0 < m < 1000000 

Output

Output the answer of (0! + 1! + 2! + 3! + 4! + ... + n!)%m. 

Sample Input

1 
10 861017 

Sample Output

593846

Hint

 

Source

山东理工大学第三届ACM程序设计竞赛