You will be given a square matrix M and a positive integer power N. You will have to compute M raised to the power N. (that is, M multiplied with itself N times.)

Input

First line of input is T (number of test-cases) First line of each test-case contains two integer M and N, where M is size of square matrix that we have to exponent and N is the power to which we have to exponent it. The next M lines describe the input matrix. Each line contains exactly M elements corresponding to each array

Output

Output M line corresponding to each row of resultant matrix Each line must have M integers where jth element of ith line is jth element of resultant matrix taken modulo with 1000000007 (10⁹+7).

Simply, you have to print the resultant square matrix.

Example

Input:
2
2 3
1 0
1 1
3 3
1 0 4
1 2 2
0 4 4

Output:
1 0
3 1
17 112 116
15 88 100
28 144 160

Constraints

1 ≤ T ≤ 10

1 ≤ M ≤ 50

1 ≤ N ≤ 100000

0 ≤ each element of input matrix ≤ 10⁹