Counting Binary Trees

There are 5 distinct binary trees of 3 nodes:

Let T(n) be the number of distinct non-empty binary trees of no more than n nodes, your task is to calculate T(n) mod m.

The input contains at most 10 test cases. Each case contains two integers n and m (1 <= n <= 100,000, 1 <= m <= 10⁹) on a single line. The input ends with n = m = 0.

For each test case, print T(n) mod m.

3 100
4 10
0 0

8
2

2009 “NIT Cup” National Invitational Contest