Domino rectangles P87164

You have 4n identical 3-3 domino pieces, and you must cover with them a 3 × 3n rectangle. As you can see in the picture below, the positions (2, 2), (2, 5), …, (2, 3n − 1) of the rectangle must be left empty. Depending on n, how many different rectangles are possible?

For instance, these are the two only possible rectangles for n = 1, two of the six possible rectangles for n = 2, and a possible rectangle for n = 7:

Input

Input consists of several cases, each with two integer numbers n and m. You can assume 0 ≤ n ≤ 10¹² and 2 ≤ m ≤ 10⁶.

Output

For every case, print the number of 3 × 3n rectangles modulo m.