I. Interval-Free Permutationstime limit per test1.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputConsider a permutation p_1, p_2, \dots p_n of integers from 1 to n. We call a sub-segment p_l, p_{l+1}, \dots, p_{r-1}, p_{r} of the permutation an interval if it is a reordering of some set of consecutive integers. For example, the permutation (6,7,1,8,5,3,2,4) has the intervals (6,7), (5,3,2,4), (3,2), and others. Each permutation has some trivial intervals — the full permutation itself and every single element. We call a permutation interval-free if it does not have non-trivial intervals. In other words, interval-free permutation does not have intervals of length between 2 and n - 1 inclusive. Your task is to count the number of interval-free permutations of length n modulo prime number p. InputIn the first line of the input there are two integers t (1 \le t \le 400) and p (10^8 \le p \le 10^9) — the number of test cases to solve and the prime modulo. In each of the next t lines there is one integer n (1 \le n \le 400) — the length of the permutation. OutputFor each of t test cases print a single integer — the number of interval-free permutations modulo p. ExamplesInput
4 998244353
1
4
5
9
Output
1
2
6
28146
Input
1 437122297
20
Output
67777575
NoteFor n = 1 the only permutation is interval-free. For n = 4 two interval-free permutations are (2,4,1,3) and (3,1,4,2). For n = 5 — (2,4,1,5,3), (2,5,3,1,4), (3,1,5,2,4), (3,5,1,4,2), (4,1,3,5,2), and (4,2,5,1,3). We will not list all 28146 for n = 9, but for example (4,7,9,5,1,8,2,6,3), (2,4,6,1,9,7,3,8,5), (3,6,9,4,1,5,8,2,7), and (8,4,9,1,3,6,2,7,5) are interval-free.The exact value for n = 20 is 264111424634864638. 
4 998244353
1
4
5
9

1 2 6 28146 
['combinatorics', '*2600']