{"raw_statement":[{"iden":"problem statement","content":"You are given positive integers $N$ and $K$. Find the number, modulo $998244353$, of integer sequences $\\bigl(f(0), f(1), \\ldots, f(2^N-1)\\bigr)$ that satisfy all of the following conditions:\n\n*   $0\\leq f(x)\\leq K$ for all non-negative integers $x$ ($0\\leq x \\leq 2^N-1$).\n*   $f(x) + f(y) = f(x \\,\\mathrm{AND}\\, y) + f(x \\,\\mathrm{OR}\\, y)$ for all non-negative integers $x$ and $y$ ($0\\leq x, y \\leq 2^N-1$)\n\nHere, $\\mathrm{AND}$ and $\\mathrm{OR}$ denote the bitwise AND and OR, respectively."},{"iden":"constraints","content":"*   $1\\leq N\\leq 3\\times 10^5$\n*   $1\\leq K\\leq 10^{18}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$"},{"iden":"sample input 1","content":"2 1"},{"iden":"sample output 1","content":"6\n\nThe following six integer sequences satisfy the conditions:\n\n*   $(0,0,0,0)$\n*   $(0,1,0,1)$\n*   $(0,0,1,1)$\n*   $(1,0,1,0)$\n*   $(1,1,0,0)$\n*   $(1,1,1,1)$"},{"iden":"sample input 2","content":"2 2"},{"iden":"sample output 2","content":"19"},{"iden":"sample input 3","content":"100 123456789123456789"},{"iden":"sample output 3","content":"34663745"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}