The following rules define a kind of integer tuple - the Legend Tuple:
- (1, k) is always a Legend Tuple, where k is an integer.
- if (n, k) is a Legend Tuple, (n + k, k) is also a Legend Tuple.
- if (n, k) is a Legend Tuple, (nk, k) is also a Legend Tuple.
We want to know the number of the Legend Tuples (n, k) where

.
In order to avoid calculations of huge integers, report the answer modulo

instead.
输入描述:
The input contains two integers N and K,
.
输出描述:
Output the answer modulo
.