{"raw_statement":[{"iden":"problem statement","content":"For a permutation $Q=(Q_1,Q_2,\\dots,Q_N)$ of $(1,2,\\dots,N)$, let $f(Q)$ be the following value:\n\n> the sum of $j-i$ over all pairs of integers $(i,j)$ such that $1 \\le i < j \\le N$ and $Q_i > Q_j$.\n\nYou are given a permutation $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$.\nLet us repeat the following operation $M$ times.\n\n*   Choose a pair of integers $(i,j)$ such that $1 \\le i \\le j \\le N$. Reverse $P_i,P_{i+1},\\dots,P_j$. Formally, replace the values of $P_i,P_{i+1},\\dots,P_j$ with $P_j,P_{j-1},\\dots,P_i$ simultaneously.\n\nThere are $\\left(\\frac{N(N+1)}{2}\\right)^{M}$ ways to repeat the operation. Assume that we have computed $f(P)$ for all those ways.\nFind the sum of these $\\left(\\frac{N(N+1)}{2}\\right)^{M}$ values, modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\le N,M \\le 2 \\times 10^5$\n*   $(P_1,P_2,\\dots,P_N)$ is a permutation of $(1,2,\\dots,N)$."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$\n$P_1$ $P_2$ $\\dots$ $P_N$"},{"iden":"sample input 1","content":"2 1\n1 2"},{"iden":"sample output 1","content":"1\n\nThere are three ways to perform the operation, as follows.\n\n*   Choose $(i,j)=(1,1)$, making $P=(1,2)$, where $f(P)=0$.\n*   Choose $(i,j)=(1,2)$, making $P=(2,1)$, where $f(P)=1$.\n*   Choose $(i,j)=(2,2)$, making $P=(1,2)$, where $f(P)=0$.\n\nThus, the answer is $0+1+0=1$."},{"iden":"sample input 2","content":"3 2\n3 2 1"},{"iden":"sample output 2","content":"90"},{"iden":"sample input 3","content":"10 2023\n5 8 1 9 3 10 4 7 2 6"},{"iden":"sample output 3","content":"543960046"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}