Matrix power

You are given an $N \times N$ matrix $A$ and an exponent $B$. Write a program that computes $A^B$.

The entries can grow very large, so print each entry of $A^B$ modulo 1,000.

The first line contains the matrix size $N$ and the exponent $B$, separated by a space. ($2 \le N \le 5$, $1 \le B \le 100{,}000{,}000{,}000$)

Each of the next $N$ lines contains one row of $A$. Every entry is 0 or a positive integer not greater than 1,000.

Print $A^B$ on $N$ lines. Line $i$ holds the $N$ entries of row $i$ separated by single spaces, each reduced modulo 1,000.