{"problem":{"name":"Tak and Cards","description":{"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 selec","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc060_a"},"statements":[{"statement_type":"Markdown","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?\n\n## Constraints\n\n*   $1 \\leq N \\leq 50$\n*   $1 \\leq A \\leq 50$\n*   $1 \\leq x_i \\leq 50$\n*   $N,\\,A,\\,x_i$ are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $A$\n$x_1$ $x_2$ $...$ $x_N$\n\n## Partial Score\n\n*   $200$ points will be awarded for passing the test set satisfying $1 \\leq N \\leq 16$.\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc060_a","tags":[],"sample_group":[["4 8\n7 9 8 9","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."],["3 8\n6 6 9","0"],["8 5\n3 6 2 8 7 6 5 9","19"],["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","8589934591\n\n*   The answer may not fit into a $32$\\-bit integer."]],"created_at":"2026-03-03 11:01:13"}}