0082. Nice Patterns Strike Back

Input file name:	nice.in
Output file name:	nice.out
Time limit:	1 s
Memory limit:	16 megabytes

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.

Input file

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

Output file

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

Examples:

nice.in	nice.out
2 2 5	4
3 3 23	0

Source: Petrozavodsk Winter 2003. St. Petersburg Contest II, Thursday, February 06

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