Cyclic Shift Sort

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.

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

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

inputFormat

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.

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

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.

outputFormat

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

样例

3 2
1 2 3

Yes