You have n distinct objects, x identical bags, and y identical boxes. In how many ways is it possible to distribute the objects into the bags and the boxes so that each bag has at least one object, and each box has exactly one object?

Input

Input consists of several test cases, each one consisting of n, x and y. Assume 1 ≤ n ≤ 25, 0 ≤ x ≤ 25, and 0 ≤ y ≤ 25.

Output

For every test case,
print the number of ways to distribute n distinct objects
into x identical bags and y identical boxes
so that each bag has at least one object,
and each box has exactly one object.
You can assume that the answer is never larger than 5 · 10^{18}.

Public test cases

**Input**

4 0 4 4 1 0 4 2 0 4 4 0 4 1 2 4 0 3 25 9 2

**Output**

1 1 7 1 6 0 3696020643539070000

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++ Python