{"raw_statement":[{"iden":"problem statement","content":"There are $N$ white balls. First, you paint each ball red or blue.\nThen, you place these $N$ red or blue painted balls in one of $M$ distinguishable boxes.\nLet $a_i$ and $b_i$ be the number of red and blue balls in the $i$\\-th box, respectively.\nFind the sum, modulo $998244353$, of $\\prod_{1\\leq i \\le M}|a_i-b_i|$ over all ways to place the balls.\nHere, two ways of placing balls are different if and only if at least one of $a_i$ and $b_i$ is different for some $i$.\nParticularly, **balls are not distinguished from each other**."},{"iden":"constraints","content":"*   $1 \\le N,M \\le 10^7$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"2 1"},{"iden":"sample output 1","content":"4\n\nThere are three ways to place balls in box $1$.  \nIf you place one red ball and one blue ball, $|a_1-b_1|=0$.  \nIf you place two red balls or two blue balls, $|a_1-b_1|=2$.  \nTherefore, the answer is $0 + 2 + 2 = 4$."},{"iden":"sample input 2","content":"5 7"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"10000000 5000000"},{"iden":"sample output 3","content":"965172629"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}