{"problem":{"name":"Constrained Nim 2","description":{"content":"There are $N$ piles of stones. Initially, the $i$\\-th pile contains $A_i$ stones. With these piles, Taro the First and Jiro the Second play a game against each other. Taro the First and Jiro the Secon","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc297_g"},"statements":[{"statement_type":"Markdown","content":"There are $N$ piles of stones. Initially, the $i$\\-th pile contains $A_i$ stones. With these piles, Taro the First and Jiro the Second play a game against each other.\nTaro the First and Jiro the Second make the following move alternately, with Taro the First going first:\n\n*   Choose a pile of stones, and remove between $L$ and $R$ stones (inclusive) from it.\n\nA player who is unable to make a move loses, and the other player wins. Who wins if they optimally play to win?\n\n## Constraints\n\n*   $1\\leq N \\leq 2\\times 10^5$\n*   $1\\leq L \\leq R \\leq 10^9$\n*   $1\\leq A_i \\leq 10^9$\n*   All values in the input are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $L$ $R$ \n$A_1$ $A_2$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc297_g","tags":[],"sample_group":[["3 1 2\n2 3 3","First\n\nTaro the First can always win by removing two stones from the first pile in his first move."],["5 1 1\n3 1 4 1 5","Second"],["7 3 14\n10 20 30 40 50 60 70","First"]],"created_at":"2026-03-03 11:01:14"}}