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 <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#define SIZE 100005

using namespace std;

int A[SIZE];
bool use[SIZE];
vector <int> query[SIZE];
int dp[SIZE];

int main()
{
	int n,m,q;
	scanf("%d %d",&n,&m);
	scanf("%d",&q);
	for(int i=0;i<q;i++)
	{
		scanf("%d",&A[i]);
		A[i]--;
		query[A[i]].push_back(i);
	}
	vector <int> ord;
	for(int i=q-1;i>=0;i--)
	{
		if(!use[A[i]])
		{
			ord.push_back(A[i]);
			use[A[i]]=true;
		}
	}
	for(int i=0;i<m;i++) if(!use[i]) ord.push_back(i);
	while(ord.size()>=2)
	{
		int sz=ord.size();
		if(ord[sz-2]>ord[sz-1]) break;
		ord.pop_back();
	}ord.pop_back();
	//for(int i=0;i<ord.size();i++) printf("%d ",ord[i]);puts("");
	for(int i=0;i<n;i++) dp[i]=q;
	for(int i=0;i<ord.size();i++)
	{
		int v=ord[i];
		int now=0;
		for(int j=((int) query[v].size())-1;j>=0;j--)
		{
			int p=query[v][j];
			if(dp[now]>p)
			{
				dp[now]=p;
				now++;
				if(now==n) break;
			}
		}
		if(now<n)
		{
			puts("No");
			return 0;
		}
	}
	puts("Yes");
	return 0;
}
