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 <cstdio>

int N,M,Q;
int as[199999];
int result[199999];
int pos[199999];
int used[199999];
int added[199999];
int ok[199999];
int main() {
	scanf("%d%d%d",&N,&M,&Q);
	for(int i=1;i<=Q;i++) scanf("%d",&as[i]);
	int rlen=1;
	for(int i=Q;i>0;i--) {
		if(used[as[i]]==0) {
			used[as[i]]=1;
			result[rlen++]=as[i];
		}
	}
	for(int i=1;i<=M;i++) if(used[i]==0) result[rlen++]=i;
	int ed=0;
	for(int i=1;i<M;i++) if(result[i]>result[i+1]) ed=i;
	for(int i=1;i<=M;i++) pos[result[i]]=i;
	ok[0]=N;
	for(int i=Q;i>0;i--) {
		int nw=pos[as[i]];
		if(nw<=ed) {
			if(ok[nw]<ok[nw-1]) ok[nw]++;
		}
	}
	for(int i=1;i<=ed;i++) if(ok[i]<N) {
		printf("No\n");
		return 0;
	}
	printf("Yes\n");
	return 0;
}
