Problem Statement

You are given a length-$N$ integer sequence $A=(A_1,A_2,\ldots,A_N)$.

You will perform the following operation on $A$ exactly once.

• Choose an integer $i$ between $1$ and $N-K+1$, inclusive. Sort $A_i,A_{i+1},\ldots,A_{i+K-1}$ in ascending order. More formally, let $B_1,B_2,\ldots,B_K$ be $A_i,A_{i+1},\ldots,A_{i+K-1}$ arranged in increasing order, and simultaneously replace $A_{i+j-1}$ with $B_j$ for $1\le j\le K$.

Determine whether it is possible that, after this operation, $A$ is in ascending order, that is, $A_i\le A_{i+1}$ holds for all $1\le i\lt N$.

Constraints

• $1\le K\lt N\le2\times10^5$
• $1\le A_i\le N\ (1\le i\le N)$
• All input values are integers.

Input

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

• $N$ $K$
• $A_1$ $A_2$ $\ldots$ $A_N$

Output

If $A$ can be sorted in ascending order by performing the operation once, output Yes; otherwise, output No.

9 6
1 4 1 4 2 1 3 5 6

Yes

For example, if you choose $2$ as $i$, then $(A_2,A_3,A_4,A_5,A_6,A_7)=(4,1,4,2,1,3)$ is replaced with $(1,1,2,3,4,4)$. After the operation, $A$ is $(1,1,1,2,3,4,4,5,6)$, which satisfies the condition.

Thus, output Yes.

3 1
3 2 1

No

$K=1$, so $A$ does not change regardless of which $i$ the operation is performed on. Thus, output No.

30 25
1 2 2 22 14 10 14 10 18 5 15 8 17 22 10 17 11 25 13 16 9 19 26 7 11 12 23 3 30 30

Yes

• Source: AtCoder ABC 478 C