{"raw_statement":[{"iden":"problem statement","content":"You are given a sequence of positive integers $A=(A_1,A_2,\\dots,A_N)$ of length $N$ and a positive integer $M$. Find the number, modulo $998244353$, of non-empty and not necessarily contiguous subsequences of $A$ such that the least common multiple (LCM) of the elements in the subsequence is $M$. Two subsequences are distinguished if they are taken from different positions in the sequence, even if they coincide as sequences. Also, the LCM of a sequence with a single element is that element itself."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq M \\leq 10^{16}$\n*   $1 \\leq A_i \\leq 10^{16}$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $A_2$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"4 6\n2 3 4 6"},{"iden":"sample output 1","content":"5\n\nThe subsequences of $A$ whose elements have an LCM of $6$ are $(2,3),(2,3,6),(2,6),(3,6),(6)$; there are five of them."},{"iden":"sample input 2","content":"5 349\n1 1 1 1 349"},{"iden":"sample output 2","content":"16\n\nNote that even if some subsequences coincide as sequences, they are distinguished if they are taken from different positions."},{"iden":"sample input 3","content":"16 720720\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16"},{"iden":"sample output 3","content":"2688"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}