Same quantity, sum and product#6086
Your task is to write a program, which will count how many different multisets have elements with sum and product (1 \le N \le 2^5 = 32, 1 \le S \le 2^{15} = 32768 and 1 \le P \le 2^{36} = 68719476736).
Two multisets are considered different when they differ by elements or by quantities of some elements. If two sequences differ by elements' order only, they are the same multiset.
Input contains three space-separated integers , and in the same line.
1 \le N \le 2^5 = 32, 1 \le S \le 2^{15} = 32768 and 1 \le P \le 2^{36} = 68719476736.
Output exactly one integer number — the quantity of different multisets.
Example 1
The multisets for st test case are:
1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9
1\ 2\ 3\ 4\ 6\ 6\ 6\ 7\ 10
1\ 2\ 4\ 4\ 4\ 5\ 7\ 9\ 9
1\ 3\ 3\ 3\ 4\ 6\ 7\ 8\ 10
1\ 3\ 3\ 4\ 4\ 4\ 7\ 9\ 10
1\ 3\ 3\ 4\ 4\ 5\ 6\ 7\ 12
2\ 2\ 2\ 3\ 4\ 6\ 7\ 9\ 10
2\ 2\ 2\ 3\ 5\ 6\ 6\ 7\ 12
2\ 2\ 3\ 3\ 3\ 5\ 7\ 8\ 12
2\ 2\ 3\ 3\ 4\ 5\ 6\ 6\ 14
2\ 3\ 3\ 3\ 3\ 4\ 5\ 8\ 14
2\ 3\ 3\ 3\ 4\ 4\ 4\ 7\ 15