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>
const int max0=100010;
int n,m,a,i;
	int countx[max0],data[max0],ans[max0],top;
	int dic[max0];
	bool had[max0],wrong;
int main()
{

	scanf("%d%d%d",&n,&m,&a);
	for(i=0;i<a;i++)
		scanf("%d",&data[i]);
	for(i=a-1;i>=0;i--)
		if(had[data[i]]==0){
                had[data[i]]=1,ans[top++]=data[i];
		}
    for(i=1;i<=m;i++)
        if(had[i]==0){
                had[i]=1,ans[top++]=i;
		}
    //printf("!%d %d %d\n",top,ans[1],p1);
	while(top>1&&ans[top-1]>ans[top-2])top--;
	if(ans[top-1]==1)top--;
    //printf("!%d\n",top);
	for(i=top-1;i>=1;i--)dic[ans[i]]=ans[i-1];
	for(i=a-1;i>=0;i--){
		countx[data[i]]++;
		if(dic[data[i]]!=0)
			if(countx[data[i]]>countx[dic[data[i]]])
				countx[data[i]]=countx[dic[data[i]]];
	}
	if(top!=0&&countx[ans[top-1]]<n)printf("No\n");
	else 	printf("Yes\n");
	return 0;
}
