{"raw_statement":[{"iden":"problem statement","content":"Tak has $N$ cards. On the $i$\\-th $(1 \\leq i \\leq N)$ card is written an integer $x_i$. He is selecting one or more cards from these $N$ cards, so that the average of the integers written on the selected cards is exactly $A$. In how many ways can he make his selection?"},{"iden":"constraints","content":"*   $1 \\leq N \\leq 50$\n*   $1 \\leq A \\leq 50$\n*   $1 \\leq x_i \\leq 50$\n*   $N,\\,A,\\,x_i$ are integers."},{"iden":"partial score","content":"*   $200$ points will be awarded for passing the test set satisfying $1 \\leq N \\leq 16$."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $A$\n$x_1$ $x_2$ $...$ $x_N$"},{"iden":"sample input 1","content":"4 8\n7 9 8 9"},{"iden":"sample output 1","content":"5\n\n*   The following are the $5$ ways to select cards such that the average is $8$:\n    *   Select the $3$\\-rd card.\n    *   Select the $1$\\-st and $2$\\-nd cards.\n    *   Select the $1$\\-st and $4$\\-th cards.\n    *   Select the $1$\\-st, $2$\\-nd and $3$\\-rd cards.\n    *   Select the $1$\\-st, $3$\\-rd and $4$\\-th cards."},{"iden":"sample input 2","content":"3 8\n6 6 9"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"8 5\n3 6 2 8 7 6 5 9"},{"iden":"sample output 3","content":"19"},{"iden":"sample input 4","content":"33 3\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3"},{"iden":"sample output 4","content":"8589934591\n\n*   The answer may not fit into a $32$\\-bit integer."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}