After a long journey home, the hare Xeni decided to play a game on her bunny phone.
The level in the game is described by an array of length and an integer . In one move, you can take adjacent elements of the array whose sum equals and remove them. After that, the size of the array will decrease by . You win the level if, after a certain number of moves, the array becomes empty.
The current level seemed very difficult to her, and she even doubted whether it was possible to complete it --- after all, there might be a situation where the game creators did not come up with more levels and made the last level impossible. Xeni turned to you for help --- tell her if it is possible to complete this game.
输入格式
The first line contains two integers , --- the size of the array and the sum of the elements to be removed (, ).
The second line of each test case contains numbers --- the elements of the game array ().
输出格式
Print , if Xeni can complete the level, and otherwise.
