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 <iostream>
using namespace std;

int main(int argc, char *argv[]){
  int N, M, Q;
  cin >> N >> M;
  cin >> Q;
  int i, j;
  int a[Q];
  for(i=0; i<Q; ++i){
    cin >> a[i];
  }
  int ind[M];
  for(i=0;i<M;++i){ind[i] = -1;}
  int laststock = 0;
  int lastcount[M];
  int before[M];
  int bef = -1;
  for(i=Q-1; i>=0; --i){
    int index = ind[a[i]-1];
    if(index == -1){
      ind[a[i]-1] = laststock;
      lastcount[laststock] = 1;
      laststock++;
    }else{
      if(index == 0 || lastcount[index] < lastcount[index-1]){
        lastcount[index]++;
      }
    }
  }
  int maxind = -1;
  int maxcover = N;
  for(i=0; i<M; ++i){
    if(ind[i] < 0){break;}
    bool f1 = false;
    bool f2 = false;
    if(ind[i] > maxind){
      maxind = ind[i];
      f1 = true;
    }
    if(lastcount[ind[i]] <= maxcover){
      maxcover = lastcount[ind[i]];
      f2 = true;
    }
    if(f1 && f2){
      lastcount[ind[i]] = N;
    }
  }
  bool ans = true;
  for(i=0; i<laststock; ++i){
    if(lastcount[i] < N){
      ans = false;
    }
  }
  if(ans){
    cout << "Yes" << endl;
  }else{
    cout << "No" << endl;
  }
  return 0;
}