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 <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int MAXN=100005;
int n,m,q,a[MAXN],pos[MAXN],beg=0,dest[MAXN];
bool vis[MAXN];
int cnt[MAXN];
int main()
{
	scanf("%d%d",&n,&m);
	scanf("%d",&q);
	for(int i=1;i<=q;++i)
		scanf("%d",a+i);
	for(int i=q;i>0;--i){
		if(!vis[a[i]]){
			pos[a[i]]=++beg;
			dest[beg]=a[i];
			vis[a[i]]=true;
		}
	}
	int t=0;
	for(int i=1;i<=m;++i)
		if(!vis[i])dest[beg+(++t)]=i;
	cnt[0]=n;
	int mx=0;
	for(int i=q;i>0;--i){
		int o=pos[a[i]];
		if(cnt[o-1]){
			--cnt[o-1];
			++cnt[o];
			mx=max(mx,o);
		}else if(mx<o-1){
			puts("No");
			return 0;
		}
	}	
	int st=n;
	for(int i=0;i<=beg;++i)
		if(cnt[i]){st=i;break;}
	for(int i=st+2;i<=m;++i)
		if(dest[i]<dest[i-1]){
			puts("No");
			return 0;
		}
	puts("Yes");
	return 0;
}
