{"problem":{"name":"Stones","description":{"content":"There is a set $A = { a_1, a_2, \\ldots, a_N }$ consisting of $N$ positive integers. Taro and Jiro will play the following game against each other. Initially, we have a pile consisting of $K$ stones. T","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"dp_k"},"statements":[{"statement_type":"Markdown","content":"There is a set $A = { a_1, a_2, \\ldots, a_N }$ consisting of $N$ positive integers. Taro and Jiro will play the following game against each other.\nInitially, we have a pile consisting of $K$ stones. The two players perform the following operation alternately, starting from Taro:\n\n*   Choose an element $x$ in $A$, and remove exactly $x$ stones from the pile.\n\nA player loses when he becomes unable to play. Assuming that both players play optimally, determine the winner.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 100$\n*   $1 \\leq K \\leq 10^5$\n*   $1 \\leq a_1 < a_2 < \\cdots < a_N \\leq K$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$a_1$ $a_2$ $\\ldots$ $a_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"dp_k","tags":[],"sample_group":[["2 4\n2 3","First\n\nIf Taro removes three stones, Jiro cannot make a move. Thus, Taro wins."],["2 5\n2 3","Second\n\nWhatever Taro does in his operation, Jiro wins, as follows:\n\n*   If Taro removes two stones, Jiro can remove three stones to make Taro unable to make a move.\n*   If Taro removes three stones, Jiro can remove two stones to make Taro unable to make a move."],["2 7\n2 3","First\n\nTaro should remove two stones. Then, whatever Jiro does in his operation, Taro wins, as follows:\n\n*   If Jiro removes two stones, Taro can remove three stones to make Jiro unable to make a move.\n*   If Jiro removes three stones, Taro can remove two stones to make Jiro unable to make a move."],["3 20\n1 2 3","Second"],["3 21\n1 2 3","First"],["1 100000\n1","Second"]],"created_at":"2026-03-03 11:01:14"}}