Consider an n-by-n matrix A. We define Ak = A ∗ A ∗ ... ∗ A (k times). Here, ∗ denotes the usual matrix multiplication. You are to write a program that computes the matrix A+A2 +A3 +...+Ak. Example 020 020 020 004 SupposeA=0 0 2.ThenA2=0 0 20 0 2=0 0 0,thus: 000 000 000 000 020 004 024 A+A2=0 0 2+0 0 2=0 0 2 000 000 000 Such computation has various applications. For instance, the above example actually counts all the paths in the following graph: Input Input consists of no more than 20 test cases. The first line for each case contains two positive integers n (≤ 40) and k (≤ 1000000). This is followed by n lines, each containing n non-negative integers, giving the matrix A. Input is terminated by a case where n = 0. This case need NOT be processed. Output For each case, your program should compute the matrix A + A2 + A3 + . . . + Ak . Since the values may be very large, you only need to print their last digit. Print a blank line after each case. Sample Input 32 020 002 000 00

2/2 Sample Output 024 002 000