Bags and boxes P75142


Statement
 

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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 · 1018.

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++
    Event
    Vuitè Concurs de Programació de la UPC - Semifinal
    Date
    2010-06-30