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Cheat in the Game
Alice and Bob are playing a game. At the beginning, the judge takes out a stone pile of W stones and a black box containing N cards. Every card has a number Ai on it. Alice and Bob takes turns to draw a card from the box. Of course, they will not know the number until they draw the card out of the box. The player then takes away Ai stones from the pile if it is possible. If there are not enough stones, the player draws a card again. The winner is the player who takes away the last stone. Once the box gets empty, they brings back all cards and stones and play the game again until there is a winner.
Now your best friend Alice begs you, the judge, to help her cheat in the game. You have already known the number of cards in the box and their numbers. Given a integer M, You want to know how many values, less or equal to M, W can take so that you can make sure Alice will be the winner of the game.
There are several test cases.
For each test case output how many values you can choose for W so that Alice will be the winner without fail.
3 8 1 5 7 0 0
We say that Alice is surely to win if and only if the possibility that Alice wins is greater than zero and the possibility that Bob wins is zero. For the sample, W = 1, 5, 7.
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