Problem Description
When Tonyfang was studying monotonous queues, he came across the following problem:
For a permutation of length n a1,a2...an, define li as maximum x satisfying xai, or 0 if such x not exists, ri as minimum x satisfying x>i and ax>ai, or n+1 if not exists. Output ∑ni=1min(i−li,ri−i).
Obviously, this problem is too easy for Tonyfang. So he thought about a harder version:
Given two integers n and x, counting the number of permutations of 1 to n which ∑ni=1min(i−li,ri−i)=x where l and r are defined as above, output the number mod P.
Tonyfang solved it quickly, now comes your turn!
Input
In the first line, before every test case, an integer P.
There are multiple test cases, please read till the end of input file.
For every test case, a line contain three integers n and x, separated with space.
1≤n≤200,1≤x≤109. P is a prime and 108≤P≤109, No more than 10 test cases.
Output
For every test case, output the number of valid permutations modulo P.
Sample Input
998244353
3 4
3 233
Sample Output
2
0
