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 $A_{P_i} \\lt A_{P_{i + 1}}$.

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.

Input

Input is given from Standard Input in the following format:

$N$ $K$ $A_1$ $\\ldots$ $A_N$

Output

Print the answer.

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