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<set>
using namespace std;
int p[110000];
int sh[110000];
pair<int,int> lat[110000];
int goal[110000];
int num[110000];
int rev[110000];
int main(){
	int a,b;scanf("%d%d",&a,&b);
	int c;scanf("%d",&c);
	for(int i=0;i<c;i++){
		scanf("%d",p+i);
		p[i]--;
	}
	for(int i=0;i<b;i++)sh[i]=-1;
	
	for(int i=c-1;i>=0;i--){
		if(sh[p[i]]==-1){
			sh[p[i]]=i;
		}
	}
	for(int i=0;i<b;i++)lat[i]=make_pair(-sh[i],i);
	std::sort(lat,lat+b);
	for(int i=0;i<b;i++)goal[i]=lat[i].second;
	for(int i=0;i<b;i++)rev[goal[i]]=i;
	bool ok=true;
//	for(int i=0;i<b;i++)printf("%d\n",p[i]);
	for(int i=c-1;i>=0;i--){
		if(rev[p[i]]==0||num[rev[p[i]]]<num[rev[p[i]]-1]){
			num[rev[p[i]]]++;
		}
	}
	int fp=99999999;
	for(int i=0;i<b;i++){
		if(num[i]<a){
			fp=i;break;
		}
	}
	for(int i=fp;i<b-1;i++){
		if(goal[i]>goal[i+1])ok=false;
	}
	if(ok)printf("Yes\n");
	else printf("No\n");
}