Eating machine (2)

Jan is an eating machine. At this moment, he is in front of a table with $c$ different kinds of cakes. He wants to eat cake exactly $n$ times, but with two restrictions:

Every kind of cake must be tasted at least once.
He wants to repeat at least with half of the kinds of cakes.

Given $n$ and $c$ , can you compute the number of ways of eating cakes? The eating order matters. For instance, if there are three kinds of cakes, say A B and C, and Jan wants to eat cake six times, these are some of the 450 possibilities: AAABBC, ABABAC, AACCBB. Note that AAAABC is not an allowed combination.

Input

Input consists of several cases, each with $n$ and $c$ . Assume $2 \le n \le 80$ , and that for each given combination there is at least one way of eating cake.

Output

For every case, print the result modulo $10^8 + 7$ .

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:50:51.646Z