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;
using Int = long long;
//INSERT ABOVE HERE
signed main(){
  Int n,m,q;
  cin>>n>>m>>q;
  vector<Int> a(q);
  for(Int i=0;i<q;i++) cin>>a[i];
  reverse(a.begin(),a.end());
  vector<Int> u(m+1,-1);
  vector<Int> v;
  vector<Int> cnt(m+1,0);
  cnt[0]=n;
  
  for(Int i=0;i<q;i++){
    if(u[a[i]]<0){
      u[a[i]]=v.size();
      v.emplace_back(a[i]);
    }
    if(cnt[u[a[i]]]){
      cnt[u[a[i]]]--;
      cnt[u[a[i]]+1]++;
    }
  }
  
  for(Int i=1;i<=m;i++)
    if(u[i]<0) v.emplace_back(i);

  for(Int i=0;i<m;i++){
    if(!cnt[i]) continue;
    Int flg=1;
    for(Int j=i;j+1<m;j++)
      flg&=v[j]<v[j+1];
    if(!flg){
      cout<<"No"<<endl;
      return 0;
    }
    break;
  }
  
  cout<<"Yes"<<endl;
  return 0;
}
