Problem Description

There are $ N $ arrays. Initially, each array has a length of $ M $ and contains integers in the order $ (1, 2, ..., M) $.

Takahashi decided to perform a total of $ Q $ operations on these $ N $ arrays. In the $ i $ -th ($1 \leq i \leq Q$) operation, he will do the following:

• Choose any one of the $ N $ arrays. In that array, move the integer $ a_i $ ($1 \leq a_i \leq M$) to the front. For example, if $ a_i = 2 $, choosing the array $ (5, 4, 3, 2, 1) $ and performing the operation will change the array to $ (2, 5, 4, 3, 1) $.

Takahashi's goal is to have all $ N $ arrays be exactly the same after the total of $ Q $ operations. Determine if it is possible for all $ N $ arrays to be exactly the same after the total of $ Q $ operations.

Input Format

The input is given from the standard input in the following format:

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

Output Format

If it is possible for all $ N $ arrays to be exactly the same after the total of $ Q $ operations, output Yes. Otherwise, output No.

Sample Input and Output

Sample Input #1

2 2
3
2 1 2

Sample Output #1

Yes

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

Sample Input #4

3 3
6
1 2 2 3 3 3

Sample Output #4

No

Notes/Hints

Constraints

• $2 \leq N \leq 10^5$
• $2 \leq M \leq 10^5$
• $1 \leq Q \leq 10^5$
• $1 \leq a_i \leq M$

Sample Explanation 1

For example, you can perform the operations as shown in the figure.

见题面 Input 部分

见题面 Output 部分