Nice Patterns Strike Back

Time Limit: 5 Seconds    Memory Limit: 32768 KB

You might have noticed that there is the new fashion among rich people to have their yards tiled with black and white tiles, forming a pattern. The company Broken Tiles is well known as the best tiling company in our region. It provides the widest choices of nice patterns to tile your yard with. The pattern is nice if there is no square of size 2 * 2, such that all tiles in it have the same color. So patterns on the figure 1 are nice, while patterns on the figure 2 are not.

The president of the company wonders whether the variety of nice patterns he can provide to the clients is large enough. Thus he asks you to find out the number of nice patterns that can be used to tile the yard of size N * M. Now he is interested in the long term estimation, so he suggests N <= 10¹⁰⁰. However, he does not like big numbers, so he asks you to find the answer modulo P.

This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.

Input

The input file contains three integer numbers: N (1 <= N <= 10¹⁰⁰), M (1 <= M <= 5) and P (1 <= P <= 10000).

Output

Write the number of nice patterns of size N * M modulo P to the output file.

Sample Input

2

2 2 5

3 3 23

Sample Output

4

0

Submit

Source: Andrew Stankevich's Contest #1