Problem Statement

You are given a permutation $P$ of $(1,2,\dots,N)$ and an integer $K$.

Find the expected value, modulo $998244353$, of the inversion number of $P$ after performing the following operation:

• First, choose an integer $i$ uniformly at random between $1$ and $N - K + 1$, inclusive.
• Then, shuffle $P_i, P_{i+1}, \dots, P_{i+K-1}$ uniformly at random.

What is the inversion number? The inversion number of a sequence $(A_1, A_2, \dots, A_N)$ is the number of integer pairs $(i, j)$ satisfying $1 \le i < j \le N$ and $A_i > A_j$.

What does "expected value modulo $998244353$" mean? It can be proved that the sought expected value is always rational. Under the constraints of this problem, when this value is represented as an irreducible fraction $\frac{P}{Q}$, it can also be proved that $Q \not\equiv 0 \pmod{998244353}$. Thus, there is a unique integer $R$ satisfying $R \times Q \equiv P \pmod{998244353}, \ 0 \le R < 998244353$. Report this integer $R$.

Constraints

• All input values are integers.
• $1 \le K \le N \le 2 \times 10^5$
• $P$ is a permutation of $(1,2,\dots,N)$.

Input

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

N K
P_1 P_2 \dots P_N

Output

Print the answer in one line.