A member a_i of the sequence a₁, a₂, ·s, a_n is called a if either a_i > a_i-1 and a_i > a_i+1 (local maximum) or a_i < a_i-1 and a_i < a_i+1 (local minimum). A sequence p₁, p₂, ·s, p_n is called a of the integers from 1 to n if each of the integers appears in the sequence exactly once. A permutation is called if each member (except the first and the last) is a local extreme.

Compute the total number of extremal permutations of the integers from 1 to n and output the result modulo m.

The first and only line of the input file contains the integers n () and m (1 ≤ m ≤ 10⁹).

The output file should contain a single integer, the remainder from division of the total number of extremal permutations of integers from 1 to n by the given integer m.

sample input	sample output
3 10	4

sample input	sample output
3 3	1

Note. The extremal permutations of 1·s3 are (1, 3, 2), (2, 1, 3), (2, 3, 1) and (3, 1, 2).