LRU Puzzle

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.

Examples

Input

2 2 3 2 1 2

Output

Yes

Input

3 2 3 2 1 2

Output

No

Input

2 3 3 3 2 1

Output

Yes

Input

3 3 6 1 2 2 3 3 3

Output

No

inputFormat

Input

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

N M Q a_1 a_2 ... a_Q

outputFormat

Output

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

Examples

Input

2 2 3 2 1 2

Output

Yes

Input

3 2 3 2 1 2

Output

No

Input

2 3 3 3 2 1

Output

Yes

Input

3 3 6 1 2 2 3 3 3

Output

No

样例

3 3
6
1 2 2 3 3 3

No