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<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int la[101010];
int p[101010];
int a[101010];
bool vis[101010];
int d[101010];
int main()
{
	int n,m,q,mi=1,cnt,lcnt,nowv,ii;
	bool mk=false;
	scanf("%d%d%d",&n,&m,&q);
	memset(la,0,sizeof(la));
	for(int i=1;i<=q;i++)
	{
		scanf("%d",&a[i]);
		p[i]=la[a[i]];
		la[a[i]]=i;
	}
	for(int i=1;i<=n;i++)
		d[i]=q+1;
	cnt=n;
	for(int i=q;i>=1;i--)
		if(a[i])
		{
			lcnt=cnt;
			cnt=0;
			nowv=a[i];
			ii=i;
			while(a[ii])
			{
				if(cnt<lcnt)
				{
					cnt++;
					if(ii<d[cnt])
						d[cnt]=ii;
					else
						cnt--;
				}
				a[ii]=0;
				ii=p[ii];
			}
			if(cnt!=n)
			{
				while(vis[mi])
					mi++;
				if(mi!=nowv)
				{
					printf("No");
					return 0;
				}
			}
			vis[nowv]=true;
		}
	printf("Yes");
	return 0;
}