# Matrix Power Series

Easy

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

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

Input #1

Answer #1

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Acceptance rate 31%