Matrix inverse
Let p a prime number. A set Fp={0,1,...,p-1} equipped with the mod p addition and multiplication is a finite field. In this problem you have to compute the multplicative inverse of some Fp valued (quadratic) matrices.
The input consists of blocks. The structure of a block is:
n p
A11...A1n
...
An1...Ann
where p is a prime number, 1<n,p<101, and Aij are in Fp. The last block followed by 0 0.
The ouput for each block is either the multiplicative inverse of a given matrix if it exists or the word "singular"
Example
Input:
4 2
1 1 1 1
1 1 0 1
0 0 0 1
0 1 0 1
3 7
3 5 0
0 5 1
6 6 6
2 2
1 1
1 0
3 5
4 0 0
2 4 1
0 2 3
3 7
0 1 4
6 1 2
2 1 1
0 0
Output:
0 1 0 1
0 0 1 1
1 1 0 0
0 0 1 0
6 3 3
5 1 1
3 3 2
0 1
1 1
singular
singular