Contest Duration: ~ (local time)
E - LRU パズル / LRU Puzzle

Time Limit: 2 sec / Memory Limit: 256 MB

問題文

• N 個の配列のうち好きなものをひとつ選ぶ。 その配列において、整数 a_i (1≤a_i≤M) を先頭へ移動する。 例えば、a_i=2 のとき、配列 (5，4，3，2，1) を選んで操作を行うと、この配列は (2，5，4，3，1) へ変わる。

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

入力

N M
Q
a_1 a_2 ... a_Q


出力

Q 回の操作の後、N 個の配列がまったく同じになるようにできるならば、Yes を出力せよ。 できないならば、No を出力せよ。

入力例 1

2 2
3
2 1 2


出力例 1

Yes


入力例 2

3 2
3
2 1 2


出力例 2

No


入力例 3

2 3
3
3 2 1


出力例 3

Yes


入力例 4

3 3
6
1 2 2 3 3 3


出力例 4

No


Score : 1200 points

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.

• 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