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 <cmath>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

int a[100010],b[100010],c[100010],s[100010];

int main()
{
	//	freopen("input.txt","r",stdin);
	//	freopen("output.txt","w",stdout);
	int n,m;scanf("%d%d",&n,&m);
	int q;scanf("%d",&q);
	for (int i=1;i<=q;i++) scanf("%d",&a[i]);
	int l=0;
	for (int i=q;i;i--)
		if (!c[a[i]])
		{
			b[++l]=a[i];c[a[i]]=l;s[a[i]]++;
		}
		else
			if (c[a[i]]==1||s[b[c[a[i]]-1]]>s[a[i]]) s[a[i]]++;
	int k=l+1;
	for (int i=1;i<=l;i++) if (s[b[i]]<n) {k=i;break;}
	for (int i=k+1;i<=l;i++) if (b[i]<b[i-1]) {puts("No");return 0;}
	for (int i=1;i<=m;i++) if (k<=l&&c[i]==0&&i<b[l]) {puts("No");return 0;}
	puts("Yes");
	return 0;
}

