codechef:April Challenge 2014: Cards, bags and coins

http://www.codechef.com/APRIL14/problems/ANUCBC

Statement

Yet another game from chef. Chef gives you N cards and M bags. Each of the N cards has an integer written on it. Now chef asks you to close your eyes and choose a subset of them. He then sums the numbers written on chosen cards, takes its absolute value and gives you those many coins. You win the game if you can divide these coins into M bags with each bag having equal share. As a first step to calculate the probability of winning, you would like to know the number of different subsets which will make you win. Note that all the cards are of different color, so even if 2 cards have the same number written on it, they are still considered as different cards.

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