{"raw_statement":[{"iden":"problem statement","content":"Given are integers $N$ and $M$. How many sequences $A$ of $N$ integers satisfy the following conditions?\n\n*   $1 \\leq A_i \\leq M \\left(i = 1, 2, \\ldots, N\\right)$\n*   $A_{i+1}$ is a multiple of $A_i$. $\\left(i = 1, 2, \\ldots, N - 1\\right)$\n\nSince the answer can be enormous, report it modulo $998244353$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq M \\leq 2 \\times 10^5$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"3 4"},{"iden":"sample output 1","content":"13\n\nSome of the sequences $A$ satisfying the conditions follow:\n\n*   $A = \\left(1, 1, 4\\right)$\n*   $A = \\left(3, 3, 3\\right)$\n*   $A = \\left(1, 2, 4\\right)$"},{"iden":"sample input 2","content":"20 30"},{"iden":"sample output 2","content":"71166"},{"iden":"sample input 3","content":"200000 200000"},{"iden":"sample output 3","content":"835917264"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}