F. Majoritytime limit per test2 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputEveryone was happy coding, until suddenly a power shortage happened and the best competitive programming site went down. Fortunately, a system administrator bought some new equipment recently, including some UPSs. Thus there are some servers that are still online, but we need all of them to be working in order to keep the round rated.Imagine the servers being a binary string s of length n. If the i-th server is online, then s_i = 1, and s_i = 0 otherwise.A system administrator can do the following operation called electricity spread, that consists of the following phases:   Select two servers at positions 1 \le i < j \le n such that both are online (i.e. s_i=s_j=1). The spread starts only from online servers.  Check if we have enough power to make the spread. We consider having enough power if the number of turned on servers in range [i, j] is at least the number of turned off servers in range [i, j]. More formally, check whether 2 \cdot (s_i + s_{i+1} + \ldots + s_j) \ge j - i + 1. If the check is positive, turn on all the offline servers in range [i, j]. More formally, make s_k := 1 for all k from i to j. We call a binary string s of length n rated if we can turn on all servers (i.e. make s_i = 1 for 1 \le i \le n) using the electricity spread operation any number of times (possibly, 0). Your task is to find the number of rated strings of length n modulo m.InputThe first and only line contains two integers n and m (1 \le n \le 5000, 10 \le m \le 10^9) — the length of the string and the required module.OutputPrint a single integer — the number of rated binary strings of length n. Since this number can be large, print it modulo m.ExamplesInput
2 100
Output
1Input
3 10
Output
2Input
4 3271890
Output
4Input
17 123456
Output
32347NoteIn the first example, the only rated string is 11. So the answer is 1.In the second example, the rated strings are:   111;  101, because we can perform an operation with i = 1 and j = 3.  So the answer is 2.In the third sample, the rated strings are:   1001;  1111;  1011;  1101.  So the answer is 4.
2 100

1
['combinatorics', 'dp', 'math', 'strings', '*2700']