{"raw_statement":[{"iden":"problem statement","content":"For a permutation $P = (p_1, p_2, \\dots, p_N)$ of $(1,2, \\dots, N)$, let us define the score $S(P)$ of $P$ as follows.\n\n*   There are $N$ people, numbered $1,2,\\dots,N$. Additionally, Snuke is there. Initially, Person $i$ $(1 \\leq i \\leq N)$ has Ball $i$.  \n    Each time Snuke screams, every Person $i$ such that $i \\neq p_i$ gives their ball to Person $p_i$ simultaneously.  \n    If, after screaming at least once, every Person $i$ has Ball $i$, Snuke stops screaming.  \n    The score is the number of times Snuke screams until he stops. Here, it is guaranteed that the score will be a finite value.\n\nThere are $N!$ permutations $P$ of $(1,2, \\dots, N)$. Find the sum, modulo $998244353$, of the scores of those permutations, each raised to the $K$\\-th power.\n\n*   Formally, let $S_N$ be the set of the permutations of $(1,2, \\dots, N)$. Compute the following: $\\displaystyle \\left(\\sum_{P \\in S_N} S(P)^K \\right) \\bmod {998244353}$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 50$\n*   $1 \\leq K \\leq 10^4$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$"},{"iden":"sample input 1","content":"2 2"},{"iden":"sample output 1","content":"5\n\nWhen $N = 2$, there are two possible permutations $P$: $(1,2),(2,1)$.\nThe score of the permutation $(1,2)$ is found as follows.\n\n*   Initially, Person $1$ has Ball $1$, and Person $2$ has Ball $2$.  \n    After Snuke's first scream, Person $1$ has Ball $1$, and Person $2$ has Ball $2$.  \n    Here, every Person $i$ has Ball $i$, so he stops screaming.  \n    Thus, the score is $1$.\n\nThe score of the permutation $(2,1)$ is found as follows.\n\n*   Initially, Person $1$ has Ball $1$, and Person $2$ has Ball $2$.  \n    After Snuke's first scream, Person $1$ has Ball $2$, and Person $2$ has Ball $1$.  \n    After Snuke's second scream, Person $1$ has Ball $1$, and Person $2$ has Ball $2$.  \n    Here, every Person $i$ has Ball $i$, so he stops screaming.  \n    Thus, the score is $2$.\n\nTherefore, the answer in this case is $1^2 + 2^2 = 5$."},{"iden":"sample input 2","content":"3 3"},{"iden":"sample output 2","content":"79\n\nAll permutations and their scores are listed below.\n\n*   $(1,2,3)$: The score is $1$.\n*   $(1,3,2)$: The score is $2$.\n*   $(2,1,3)$: The score is $2$.\n*   $(2,3,1)$: The score is $3$.\n*   $(3,1,2)$: The score is $3$.\n*   $(3,2,1)$: The score is $2$.\n\nThus, we should print $1^3 + 2^3 + 2^3 + 3^3 + 3^3 + 2^3 = 79$."},{"iden":"sample input 3","content":"50 10000"},{"iden":"sample output 3","content":"77436607"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}