Problem Statement

You are given a permutation $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$. You will perform the following operation $M$ times:

• Choose a pair of integers $(i, j)$ such that $1 \le i < j \le N$, and swap $P_i$ and $P_j$.

There are $\left(\frac{N(N-1)}{2}\right)^M$ possible sequences of operations. For each of them, consider the value $\sum_{i=1}^{N-1} |P_i - P_{i+1}|$ after all the operations. Find the sum, modulo $998244353$, of all those values.

Constraints

• $2 \le N \le 2 \times 10^5$
• $1 \le M \le 2 \times 10^5$
• $(P_1,P_2,\dots,P_N)$ is a permutation of $(1,2,\dots,N)$.

Input

The input is given from Standard Input in the following format:

N M
P_1 P_2 \dots P_N

Output

Print the answer.