Matrix Power Series

Given a n × n matrix A and a positive integer k, find the sum S = A + A^2 + A^3 + ... + A^k.

Input

The first line contains three positive integers n (n ≤ 30), k (k ≤ 10^9) and m (m < 10^4). Then follow n lines each containing n non-negative integers below 32768, giving A's elements in row-major order.

Output

Print the elements of S modulo m in the same way as A is given.

Examples