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 ≤ n ≤ 80,
and that for each given combination there is at least one way of eating
cake.

Output

For every case, print the result modulo 10⁸ + 7.

Problem information

Author: Salvador Roura

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

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