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>
#include<cstdio>
#include<algorithm>
#include<set>
#include<map>
#include<queue>
#include<cassert>
#define PB push_back
#define MP make_pair
#define sz(v) (in((v).size()))
#define forn(i,n) for(in i=0;i<(n);++i)
#define forv(i,v) forn(i,sz(v))
#define fors(i,s) for(auto i=(s).begin();i!=(s).end();++i)
#define all(v) (v).begin(),(v).end()
using namespace std;
typedef long long in;
typedef vector<in> VI;
typedef vector<VI> VVI;
in n,m,q;
vector<set<in> > lofn;
set<in> rmg;
VI lat;
VI mar;
void imp(){
  cout<<"No"<<endl;
  exit(0);
}
int main(){
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin>>n>>m;
  cin>>q;
  mar.resize(q);
  forn(i,q){
    cin>>mar[i];
    --mar[i];
  }
  lat.resize(n,q+2);
  forn(i,m)
    rmg.insert(i);
  lofn.resize(m);
  forn(i,q){
    lofn[mar[i]].insert(i);
  }
  bool isb;
  set<in>::iterator it;
  for(in i=q-1;i>=0;--i){
    if(rmg.find(mar[i])==rmg.end())
      continue;
    in u=mar[i];
    isb=(*rmg.begin()==u);
    forv(j,lat){
      it=lofn[u].upper_bound(lat[j]);
      if(it==lofn[u].begin()){
	if(!isb)
	  imp();
	if(lat[j]==-1)
	  break;
	lat[j]=-1;
	continue;
      }
      --it;
      lat[j]=*it;
      lofn[u].erase(it);
    }
    rmg.erase(u);
  }
  cout<<"Yes"<<endl;
  return 0;
}
