{"problem":{"name":"Modulo Operations","description":{"content":"Snuke has a blackboard and a set $S$ consisting of $N$ integers. The $i$\\-th element in $S$ is $S_i$. He wrote an integer $X$ on the blackboard, then performed the following operation $N$ times: *   ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"exawizards2019_d"},"statements":[{"statement_type":"Markdown","content":"Snuke has a blackboard and a set $S$ consisting of $N$ integers. The $i$\\-th element in $S$ is $S_i$.\nHe wrote an integer $X$ on the blackboard, then performed the following operation $N$ times:\n\n*   Choose one element from $S$ and remove it.\n*   Let $x$ be the number written on the blackboard now, and $y$ be the integer removed from $S$. Replace the number on the blackboard with $x \\bmod {y}$.\n\nThere are $N!$ possible orders in which the elements are removed from $S$. For each of them, find the number that would be written on the blackboard after the $N$ operations, and compute the sum of all those $N!$ numbers modulo $10^{9}+7$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 200$\n*   $1 \\leq S_i, X \\leq 10^{5}$\n*   $S_i$ are pairwise distinct.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $X$\n$S_1$ $S_2$ $\\ldots$ $S_{N}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"exawizards2019_d","tags":[],"sample_group":[["2 19\n3 7","3\n\n*   There are two possible orders in which we remove the numbers from $S$.\n*   If we remove $3$ and $7$ in this order, the number on the blackboard changes as follows: $19 \\rightarrow 1 \\rightarrow 1$.\n*   If we remove $7$ and $3$ in this order, the number on the blackboard changes as follows: $19 \\rightarrow 5 \\rightarrow 2$.\n*   The output should be the sum of these: $3$."],["5 82\n22 11 6 5 13","288"],["10 100000\n50000 50001 50002 50003 50004 50005 50006 50007 50008 50009","279669259\n\n*   Be sure to compute the sum modulo $10^{9}+7$."]],"created_at":"2026-03-03 11:01:14"}}