{"raw_statement":[{"iden":"problem statement","content":"Given is a positive integer $M$ and a sequence of $N$ integers: $A = (A_1,A_2,\\ldots,A_N)$. Find the number, modulo $998244353$, of sequences of $N+1$ integers, $X = (X_1,X_2, \\ldots, X_{N+1})$, satisfying all of the following conditions:\n\n*   $1\\leq X_i\\leq M$ ($1\\leq i\\leq N+1$)\n*   $A_iX_i\\leq X_{i+1}$ ($1\\leq i\\leq N$)"},{"iden":"constraints","content":"*   $1\\leq N\\leq 1000$\n*   $1\\leq M\\leq 10^{18}$\n*   $1\\leq A_i\\leq 10^9$\n*   $\\prod_{i=1}^N A_i \\leq M$"},{"iden":"input","content":"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":"2 10\n2 3"},{"iden":"sample output 1","content":"7\n\nSeven sequences below satisfy the conditions.\n\n*   $(1, 2, 6)$, $(1,2,7)$, $(1,2,8)$, $(1,2,9)$, $(1,2,10)$, $(1,3,9)$, $(1,3,10)$"},{"iden":"sample input 2","content":"2 10\n3 2"},{"iden":"sample output 2","content":"9\n\nNine sequences below satisfy the conditions.\n\n*   $(1, 3, 6)$, $(1, 3, 7)$, $(1, 3, 8)$, $(1, 3, 9)$, $(1, 3, 10)$, $(1, 4, 8)$, $(1, 4, 9)$, $(1, 4, 10)$, $(1, 5, 10)$"},{"iden":"sample input 3","content":"7 1000\n1 2 3 4 3 2 1"},{"iden":"sample output 3","content":"225650129"},{"iden":"sample input 4","content":"5 1000000000000000000\n1 1 1 1 1"},{"iden":"sample output 4","content":"307835847"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}