{"raw_statement":[{"iden":"problem statement","content":"For a sequence $A$ of length $N$ consisting of integers between $1$ and $M$ (inclusive), let us define $f(A)$ as follows:\n\n*   We have a sequence $X$ of length $N$, where every element is initially $0$. $f(A)$ is the minimum number of operations required to make $X$ equal $A$ by repeating the following operation:\n    *   Specify $1 \\leq l \\leq r \\leq N$ and $1 \\leq v \\leq M$, then replace $X_i$ with $\\max(X_i, v)$ for each $l \\leq i \\leq r$.\n\nFind the sum, modulo $998244353$, of $f(A)$ over all $M^N$ sequences that can be $A$."},{"iden":"constraints","content":"*   $1 \\leq N, M \\leq 5000$\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":"2 3"},{"iden":"sample output 1","content":"15\n\nThe $3 ^ 2 = 9$ sequences and the value of $f$ for those are as follows:\n\n*   For $A = (1, 1)$, we can make $X$ equal it with one operation with $(l = 1, r = 2, v = 1)$, so $f(A) = 1$.\n*   For $A = (1, 2)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 1)$ and $(l = 2, r = 2, v = 2)$, so $f(A) = 2$.\n*   For $A = (1, 3)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 1)$ and $(l = 2, r = 2, v = 3)$, so $f(A) = 2$.\n*   For $A = (2, 1)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 1)$ and $(l = 1, r = 1, v = 2)$, so $f(A) = 2$.\n*   For $A = (2, 2)$, we can make $X$ equal it with one operation with $(l = 1, r = 2, v = 2)$, so $f(A) = 1$.\n*   For $A = (2, 3)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 2)$ , $(l = 2, r = 2, v = 3)$, so $f(A) = 2$.\n*   For $A = (3, 1)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 1)$ and $(l = 1, r = 1, v = 3)$ so $f(A) = 2$.\n*   For $A = (3, 2)$, we can make $X$ equal it with two operations with $(l = 1, r = 2, v = 2)$ and $(l = 1, r = 1, v = 3)$, so $f(A) = 2$.\n*   For $A = (3, 3)$, we can make $X$ equal it with one operation with $(l = 1, r = 2, v = 3)$, so $f(A) = 1$.\n\nThe sum of these values is $3 \\times 1 + 6 \\times 2 = 15$."},{"iden":"sample input 2","content":"3 2"},{"iden":"sample output 2","content":"15"},{"iden":"sample input 3","content":"34 56"},{"iden":"sample output 3","content":"649717324"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}