Powers of a matrix

Given a $2 \times 2$ matrix $M$ of natural numbers, a natural number $n$ and a natural number $m$ , compute $M^n$ . To avoid overflows, compute every element of $M^n \bmod m$ .

Input

Input consists of several cases, each with $M_{11}$ , $M_{12}$ , $M_{21}$ and $M_{22}$ in this order, followed by $n$ and $m$ . Assume that the elements of $M$ are not larger than $500$ , $0 \le n \le 10^9$ , and $2 \le m \le 1000$ .

Output

For every case, print the elements of $M^n \bmod m$ in two lines following the format of the sample. Print a line with 10 dashes after every matrix.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:10:48.171Z