Problem

Given a permutation of length $ N $ $P = \\ {P_1, P_2, \ ldots, P_N \\}$ and the integer $ K $.
Determine if the permutation $ P $ can be monotonically increased by repeating the following operation any number of times $ 0 $ or more.

• Choose the integer $x \ (0 \ le x \ le N-K)$. Patrol right shift around $P_ {x + 1}, \ ldots, P_ {x + K}$

However, the cyclic right shift of the subsequence $U = U_1, \ ldots, U_M$ means that $U = U_1, \ ldots, U_M$ is changed to $U = U_M, U_1, \ ldots, U_ {M-1}$. Means to change.

Constraints

The input satisfies the following conditions.

• $2 \ leq K \ leq N \ leq 10 ^ 5$
• $1 \ leq P_i \ leq N \ (1 \ leq i \ leq N)$
• $P_i \ neq P_j \ (i \ neq j)$
• All inputs are integers

Input

The input is given in the following format.

$ N $ $ K $
$ P_1 $ $\$ $ P_N $

Permutation length $ N $ and integer $ K $ are given in the first row, separated by blanks.
The elements of the permutation $ P $ are given in the second row, separated by blanks.

Output

Print "Yes" if you can monotonically increase $ P $, otherwise print "No" on the $ 1 $ line.

Examples

Input

3 3
2 3 1

Output

Yes

Input

3 2
1 2 3

Output

Yes

Input

3 3
3 2 1

Output

No

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