Problem Statement

You are given an integer sequence $A = (A_1, \dots, A_N)$ of length N.
Find the number, modulo 998244353, of permutations $P = (P_1, \dots, P_N)$ of $(1, 2, \dots, N)$ such that:

• there exist exactly K integers i between 1 and (N-1) (inclusive) such that $A_{P_i} \lt A_{P_{i + 1}}$.

Input

Input is given from Standard Input in the following format:
N K
$A_1 \ldots A_N$

Output

Print the answer.

Constraints

• $2 \leq N \leq 5000$
• $0 \leq K \leq N - 1$
• $1 \leq A_i \leq N$ $, (1 \leq i \leq N)$
• All values in input are integers.

Sample Input 1

4 2
1 1 2 2

Sample Output 1

4

Four permutations satisfy the condition: P = (1, 3, 2, 4), (1, 4, 2, 3), (2, 3, 1, 4), (2, 4, 1, 3).

Sample Input 2

10 3
3 1 4 1 5 9 2 6 5 3

Sample Output 2

697112

见题面 Input 部分

见题面 Output 部分