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 <bits/stdc++.h>
using namespace std;
const int MAXN=1e5+7;
int f[MAXN],b[MAXN],n,m,q,l[MAXN],st,a[MAXN],A[MAXN];
int main()
{
	cin>>n>>m>>q;
	for(int i=1;i<=q;i++) cin>>a[i];
	for(int i=q;i>=1;i--){
		if(!b[a[i]]){
			A[++A[0]]=a[i];
			b[a[i]]=1;
		}
	}
	for(int i=1;i<=m;i++)
		if(!b[i]) A[++A[0]]=i;
	memset(b,0,sizeof(b));
	
	l[0]=n;
	for(int i=q;i>=1;i--){
		if(!b[a[i]]){
			st++;
			b[a[i]]=st;
			f[st]=a[i];
			l[st-1]--;l[st]++;
		} else if(l[b[a[i]]-1]){
			l[b[a[i]]-1]--;l[b[a[i]]]++;
		}
	}
	memset(b,0,sizeof(b));
	for(int i=0;i<st;i++){
		if(l[i]){
			st=i;
			for(int j=1;j<=i;j++){
				if(f[j]!=A[j]){
					cout<<"No"<<endl;
					return 0;
				}
				b[f[j]]=1;
			}
			for(int j=1;j<=m;j++){
				if(!b[j]){
					st++;
					if(j!=A[st]){
						cout<<"No"<<endl;
						return 0;
					}
				}
			}
			break;
		}
	}
	cout<<"Yes"<<endl;
}