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G - Increasing K Times

Score : $600$ points

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.

4 2
1 1 2 2

4

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

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

697112