Problem Description
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.
Input
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.
Output
For each test case, print T(n) mod m.
Sample Input
3 100
4 10
0 0
Sample Output
8
2