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 <cstdio>
#include <algorithm>
#include <vector>
using namespace std;

int main()
{
  int n,m,q;
  scanf("%d%d%d",&n,&m,&q);
  static int a[100010];
  for(int i=0;i<q;i++){
    scanf("%d",a+i);
    a[i]--;
  }
  bool F=1;
  static int P[100010],C[100010],T[100010];
  for(int i=0;i<m;i++){
    P[i]=-1;
  }
  int N=0;
  for(int i=q-1;i>=0;i--){
    int k=a[i];
    if(P[k]==-1){
      P[k]=N;
      C[N]=1;
      T[N]=k;
      N++;
    }
    else if(C[P[k]]<n){
      C[P[k]]++;
      if(P[k]>0&&C[P[k]-1]<C[P[k]]){
	C[P[k]]--;
      }
    }
  }
  if(F){
    vector<int> V;
    int K=0;
    for(int i=0;i<m;i++){
      if(P[i]==-1||C[P[i]]<n){
	V.push_back(i);
      }
      else{
	K++;
      }
    }
    for(int i=K;i<N;i++){
      if(T[i]!=V[i-K]){
	F=0;
      }
    }
  }
  puts(F?"Yes":"No");
  return 0;
}
