{"raw_statement":[{"iden":"problem statement","content":"The following process is carried out on a permutation $P$ of $(1,2,\\dots,N)$.\n\n> We have $N$ cards, numbered $1$ to $N$. Card $i$ has the integer $P_i$ written on it.\n> There are an integer $X=1$ and a boy called PCT, who initially has nothing. PCT does the following procedure for each $i=1,2,\\dots,N$ in this order.\n> \n> *   Get Card $i$. Then, repeat the following action as long as he has a card with $X$ written on it:\n> \n> *   eat the card with $X$ written on it, and then add $1$ to $X$.\n> \n> *   If PCT currently has $M$ or more cards, throw away all cards he has and terminate the process, without performing any more procedures.\n\nHere, let us define the score of the permutation $P$ as follows:\n\n*   if the process is terminated by throwing away cards, the score of $P$ is $0$;\n*   if the process is carried out through the end without throwing away cards, the score of $P$ is $\\prod_{i=1}^{N-1}$ $($ the number of cards PCT has at the end of the $i$\\-th procedure $)$.\n\nThere are $N!$ permutations $P$ of $(1,2,\\dots,N)$. Find the sum of the scores of all those permutations, modulo $998244353$."},{"iden":"constraints","content":"*   $2 \\le N \\le 2 \\times 10^5$\n*   $2 \\le M \\le N$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"3 2"},{"iden":"sample output 1","content":"1\n\nFor $P=(3,1,2)$, the process goes as follows.\n\n*   The first procedure:\n    *   PCT gets Card $1$.\n    *   PCT currently has $1$ card, so he goes on.\n*   The second procedure:\n    *   PCT gets Card $2$.\n    *   PCT eats Card $2$ and make $X = 2$.\n    *   PCT currently has $1$ card, so he goes on.\n*   The third procedure:\n    *   PCT gets Card $3$.\n    *   PCT eats Cards $1,3$ and make $X = 4$.\n    *   PCT currently has $0$ cards, so he goes on.\n\nThe process is carried out through the end, so the score of $(3,1,2)$ is $1 \\times 1 = 1$.\nOther than $(3,1,2)$, there is no permutation with a score of $1$ or greater, so the answer is $1$."},{"iden":"sample input 2","content":"3 3"},{"iden":"sample output 2","content":"5"},{"iden":"sample input 3","content":"146146 146"},{"iden":"sample output 3","content":"103537573"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}