{"problem":{"name":"Many Increasing Problems","description":{"content":"PCT-kun created the following problem. > **Increasing Problem**You are given a length-$N$ sequence of non-negative integers $A_1,A_2,\\dots,A_N$. You can perform the following operation any number of ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":5000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc163_f"},"statements":[{"statement_type":"Markdown","content":"PCT-kun created the following problem.\n\n> **Increasing Problem**You are given a length-$N$ sequence of non-negative integers $A_1,A_2,\\dots,A_N$. You can perform the following operation any number of times (possibly zero).\n> \n> *   Choose an integer $i$ such that $1 \\le i \\le N$, and increase or decrease $A_i$ by $1$.\n> \n> Your goal is to make $A$ non-decreasing. Find the minimum number of operations required to achieve this goal.\n\nThinking that this problem is too easy to be placed at the end of the contest, PCT-kun has revised it as follows.\n\n> **Many Increasing Problems**There are $M^N$ integer sequences $A$ of length $N$ where all elements are between $1$ and $M$, inclusive. Find the sum of the answers to **Increasing Problem** for all those sequences, modulo $998244353$.\n\nSolve **Many Increasing Problems**.\n\n## Constraints\n\n*   $1 \\le N,M \\le 10^5$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc163_f","tags":[],"sample_group":[["2 2","1\n\nLet us solve **Increasing Problem** for all sequences of length $2$ where all elements are between $1$ and $2$, inclusive.\n\n*   For $A=(1,1)$, the answer is $0$.\n*   For $A=(1,2)$, the answer is $0$.\n*   For $A=(2,1)$, the answer is $1$.\n*   For $A=(2,2)$, the answer is $0$.\n\nTherefore, the final answer is $0+0+1+0=1$."],["6 4","14668"],["163 702","20728656"],["98765 99887","103564942"]],"created_at":"2026-03-03 11:01:13"}}