Factorial Factorial
Problem
Let us define a function:
F(N, k) = (....((N!)!)!.... )! k times, where N! = 1 * 2 * 3 * .... * (N-1) * N
For eg., F(N, 2) = (N!)! and F(N, 3) = (((N)!)!)!
Given any N and k, you have to find the value of F(N, k). Since this value can be really large, print
this value modulo 107.
Input
First Line consists of T, the number of test cases. After this, T lines follow, each line consists of 2
space separated integers N followed by k.
Output
For every test case, print the value of F(N, k) % 107 on a new line.
Constraints
1 <= T <= 100
1 <= N <= 10,00,000
2 <= k <= 100
Time Limit: 2
Memory Limit: 256
Source Limit:
Explanation
Test Case 1: (((1!)!)!)! = 1, 1 % 107 = 1
Test Case 2: ((((2!)!)!)!)! = 2, 2 % 107 = 2
Test Case 3: (3!)! = 6! = 720, 720 % 107 = 78
