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;
int n,m,k,i,j,a[100100],b[100100],f[100100];
bool was[100100];
vector<int> v;
int main() {
  scanf("%d%d%d",&n,&m,&k);
  for (i=0; i<k; i++) scanf("%d",&a[i]);
  for (i=1; i<=m; i++) b[i]=-1;
  for (i=k-1; i>=0; i--) if (!was[a[i]]) {
    was[a[i]]=true;
    b[a[i]]=v.size();
    v.push_back(a[i]);
  }
  for (i=1; i<=m; i++) if (!was[i]) break;
  for (m=v.size(); m>0 && v[m-1]<i; m--) i=v[m-1];
  for (i=k-1; i>=0; i--) {
    j=b[a[i]];
    f[j]=min(n,(j>0)?min(f[j]+1,f[j-1]):(f[j]+1));
  }
  puts((m==0 || f[m-1]>=n)?"Yes":"No");
  return 0;
}
