Problem Statement

There are $N$ arrays. The length of each array is $M$ and initially each array contains integers $(1，2，...，M)$ in this order.

Mr. Takahashi has decided to perform $Q$ operations on those $N$ arrays. For the $i$-th ($1≤i≤Q$) time, he performs the following operation.

• Choose an arbitrary array from the $N$ arrays and move the integer $a_i$ ($1≤a_i≤M$) to the front of that array. For example, after performing the operation on $a_i=2$ and the array $(5，4，3，2，1)$, this array becomes $(2，5，4，3，1)$.

Mr. Takahashi wants to make $N$ arrays exactly the same after performing the $Q$ operations. Determine if it is possible or not.

Constraints

• $2≤N≤10^5$
• $2≤M≤10^5$
• $1≤Q≤10^5$
• $1≤a_i≤M$

Input

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

$N$ $M$ $Q$ $a_1$ $a_2$ $...$ $a_Q$

Output

Print Yes if it is possible to make $N$ arrays exactly the same after performing the $Q$ operations. Otherwise, print No.

Sample Input 1

2 2
3
2 1 2

Sample Output 1

Yes

You can perform the operations as follows.

Sample Input 2

3 2
3
2 1 2

Sample Output 2

No

Sample Input 3

2 3
3
3 2 1

Sample Output 3

Yes

You can perform the operations as follows.

Sample Input 4

3 3
6
1 2 2 3 3 3

Sample Output 4

No