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>
int p[100010],a[100010],pos[100010],c[100010];
bool us[100010];
int main(){
	int n,m,q,i,N;
	scanf("%d%d%d",&n,&m,&q);
	for(i=1;i<=q;i++)scanf("%d",p+i);
	N=0;
	for(i=q;i>0;i--){
		if(!us[p[i]])us[a[++N]=p[i]]=1;
	}
	for(i=1;i<=m;i++){
		if(!us[i])a[++N]=i;
	}
	for(i=1;i<=m;i++)pos[a[i]]=i;
	#define wa {puts("No");return 0;}
	c[0]=n;
	for(i=q;i>0;i--){
		if(c[pos[p[i]]-1]){
			c[pos[p[i]]-1]--;
			c[pos[p[i]]]++;
		}
	}
	for(i=0;!c[i];i++);
	for(i++;i<m;i++){
		if(a[i]>a[i+1])wa
	}
	puts("Yes");
}