{"problem":{"name":"Ex - Distinct Multiples","description":{"content":"Given are positive integers $N$, $M$, and a sequence of positive integers $D = (D_1, \\dots, D_N)$. Find the number of sequences of positive integers $A = (A_1, \\dots, A_N)$ that satisfy the following ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc236_h"},"statements":[{"statement_type":"Markdown","content":"Given are positive integers $N$, $M$, and a sequence of positive integers $D = (D_1, \\dots, D_N)$.\nFind the number of sequences of positive integers $A = (A_1, \\dots, A_N)$ that satisfy the following conditions, modulo $998244353$.\n\n*   $1 \\leq A_i \\leq M \\, (1 \\leq i \\leq N)$\n*   $A_i \\neq A_j \\, (1 \\leq i \\lt j \\leq N)$\n*   For each $i \\, (1 \\leq i \\leq N)$, $A_i$ is a multiple of $D_i$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 16$\n*   $1 \\leq M \\leq 10^{18}$\n*   $1 \\leq D_i \\leq M \\, (1 \\leq i \\leq N)$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n$D_1$ $\\ldots$ $D_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc236_h","tags":[],"sample_group":[["3 7\n2 3 4","3\n\nThe three sequences $A$ that satisfy the conditions are $(2, 3, 4), (2, 6, 4), (6, 3, 4)$."],["3 3\n1 2 2","0\n\nNo sequence $A$ satisfies the conditions."],["6 1000000000000000000\n380214083 420492929 929717250 666796775 209977152 770361643","325683519\n\nBe sure to find the count modulo $998244353$."]],"created_at":"2026-03-03 11:01:14"}}