Problem Statement

Snuke received a permutation $P=(P_1,P_2,\cdots,P_N)$ of $(1,\ 2,\ ...\ N)$ and an integer $K$. He did some number of swaps of two adjacent elements in $P$ so that the following condition would be satisfied.

• For each $1 \leq i \leq N$, there are at most $K$ indices $j$ such that $1 \leq j< i$ and $P_j>P_i$.

Here, he did the minimum number of swaps needed to achieve this condition.

Afterward, he has forgotten the original permutation he received. Given the permutation $P'$ after the swaps, find the number, modulo $998244353$, of permutations that the original permutation $P$ could be.

Constraints

• $2 \leq N \leq 5000$
• $1 \leq K \leq N-1$
• $1 \leq P'_i \leq N$
• $P'_i \neq P'_j$ ($i \neq j$)
• For each $1 \leq i \leq N$, there is at most $K$ indices $j$ such that $1 \leq j< i$ and $P'_j>P'_i$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P'_1 P'_2 \cdots P'_N

Output

Print the answer.