Parentheses and brackets P36384


Statement
 

pdf   zip

html

Suppose that you have x pairs of parentheses and y pairs of brackets. In how many ways can you correctly put the parentheses and brackets?

For example, there are 15 ways with x = 2 and y = 1:

  ()()[]     ()[()]     (()[])     ([()])     [()]()   
  ()([])     (())[]     (([]))     []()()     [()()]   
  ()[]()     ([])()     ([]())     [](())     [(())]   

The number of combinations grows very fast with x and y. Therefore, make the calculations modulo a given natural number m.

Input

Input consists of several cases. Every case has x, y and m. Suppose 0 ≤ x ≤ 50, 0 ≤ y ≤ 50, and 2 ≤ m ≤ 108.

Output

For every case, print the number of correct ways to place x pairs of parentheses and y pairs of brackets, modulo m.

Public test cases
  • Input

    2 1 1000000
    1 2 1000000
    1 2 4
    0 0 1000000
    1 0 1000000
    2 0 1000000
    3 0 1000000
    6 6 100000000
    6 6 1000
    50 50 100000000
    

    Output

    15
    15
    3
    1
    1
    2
    5
    92203088
    88
    24825920
    
  • Information
    Author
    Salvador Roura
    Language
    English
    Translator
    Salvador Roura
    Original language
    Catalan
    Other languages
    Catalan
    Official solutions
    C++
    User solutions
    C++