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
#include <stdio.h>
#include <algorithm>
#include <cmath>
#include <queue>
#include <vector>
#include <map>
#include <set>

using namespace std;

int N , M , Q;
int a[100010];
int x[100010];
int o[100010];
int c;
int f , e;

int main(){
	scanf("%d%d%d" , &N , &M , &Q);
	for(int i = 0 ; i < Q ; ++i){
		scanf("%d" , a + i);
	}
	c = 0;
	f = 0;
	e = 0;
	x[0] = N;
	for(int i = Q - 1 ; i >= 0 ; --i){
		if(o[a[i]] == 0){
			++e;
			o[a[i]] = e;
			while(o[c + 1] > 0) ++c;
			if(c < a[i]){
				f = e;
			}
		}
		if(x[o[a[i]] - 1] > x[o[a[i]]]) ++x[o[a[i]]];
	}
	for(int i = 1 ; i <= f ; ++i){
		if(x[i] < N){
			printf("No\n");
			return 0;
		}
	}
	printf("Yes\n");
	return 0;
}
