"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.

Input

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.

Output

Output exactly one integer number — the quantity of different multisets.

Examples

Note

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