Problem Statement

For $a permutation Q=(Q_1,Q_2,\dots,Q_N)$ of $(1,2,\dots,N)$, let f(Q) be the following value:

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.

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

• 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.

There 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.
Find the sum of these $\left(\frac{N(N+1)}{2}\right)^{M} values, modulo 998244353$.

Input

The input is given from Standard Input in the following format:
N M
$P_1 P_2 \dots P_N$

Output

Print a single line containing the answer.

Constraints

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

Sample Input 1

2 1
1 2

Sample Output 1

1

There are three ways to perform the operation, as follows.

• Choose (i,j)=(1,1), making P=(1,2), where f(P)=0.
• Choose (i,j)=(1,2), making P=(2,1), where f(P)=1.
• Choose (i,j)=(2,2), making P=(1,2), where f(P)=0.

Thus, the answer is 0+1+0=1.

Sample Input 2

3 2
3 2 1

Sample Output 2

90

Sample Input 3

10 2023
5 8 1 9 3 10 4 7 2 6

Sample Output 3

543960046

见题面 Input 部分

见题面 Output 部分