"Same quantity, sum and product"
"Same quantity, sum and product"
Your task is to write a program, which will count how many different multisets has N elements with sum S and product P (1 ≤ N ≤ 2^{5 }= 32, 1 ≤ S ≤ 2^{15 }= 32768 and 1 ≤ P ≤ 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.
Giriş verilənləri
Input contains three space-separated integers N, S and P in the same line.
1 ≤ N ≤ 2^5=32, 1 ≤ S ≤ 2^15=32768 and 1 ≤ P ≤ 2^36=68719476736.
Çıxış verilənləri
Output exactly one integer number — the quantity of different multisets.
Nümunə
9 45 362880
12
Qeyd
The 12 multisets for 1^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