{"raw_statement":[{"iden":"problem statement","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 $10^{9}+7$."},{"iden":"constraints","content":"*   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."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $X$\n$S_1$ $S_2$ $\\ldots$ $S_{N}$"},{"iden":"sample input 1","content":"2 19\n3 7"},{"iden":"sample output 1","content":"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: $3$."},{"iden":"sample input 2","content":"5 82\n22 11 6 5 13"},{"iden":"sample output 2","content":"288"},{"iden":"sample input 3","content":"10 100000\n50000 50001 50002 50003 50004 50005 50006 50007 50008 50009"},{"iden":"sample output 3","content":"279669259\n\n*   Be sure to compute the sum modulo $10^{9}+7$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}