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;
#define PB push_back
#define MP make_pair
#define LL long long
#define int LL
#define FOR(i,a,b) for(int i = (a); i <= (b); i++)
#define RE(i,n) FOR(i,1,n)
#define REP(i,n) FOR(i,0,(int)(n)-1)
#define R(i,n) REP(i,n)
#define VI vector<int>
#define PII pair<int,int>
#define LD long double
#define FI first
#define SE second
#define st FI
#define nd SE
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())

template<class C> void mini(C& _a4, C _b4) { _a4 = min(_a4, _b4); }
template<class C> void maxi(C& _a4, C _b4) { _a4 = max(_a4, _b4); }

template<class TH> void _dbg(const char *sdbg, TH h){ cerr<<sdbg<<'='<<h<<endl; }
template<class TH, class... TA> void _dbg(const char *sdbg, TH h, TA... a) {
  while(*sdbg!=',')cerr<<*sdbg++;cerr<<'='<<h<<','; _dbg(sdbg+1, a...);
}

template<class T> ostream& operator<<(ostream& os, vector<T> V) {
  os << "["; for (auto& vv : V) os << vv << ","; os << "]";
  return os;
}

#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (__VA_ARGS__)
#define cerr if(0)cout
#endif

const int MAX = 101001;
vector<int> t,co;
int dp[MAX];
int cz[MAX];
int il = 0;
int kt[MAX];
int n,m,q;
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout << fixed << setprecision(11);
  cerr << fixed << setprecision(6);
  cin >> n >> m >> q;
  R(i,q){
    int pom;
    cin >> pom;
    pom--;
    t.PB(pom);
  }
  reverse(ALL(t));
  for(int el:t){
    if(!cz[el]){
      cz[el] = 1;
      kt[el] = il;
      il++;
      co.PB(el);
    }
    int pom = kt[el];
    dp[pom]++;
    if(pom != 0)
      mini(dp[pom],dp[pom-1]);
  }
  int naj = 0;
  while(cz[naj])naj++;
  debug(naj);
  while(!co.empty() && naj > co.back()){
    naj = co.back();
    co.pop_back();
  }
  il = SZ(co);
  debug(il);
  if(il == 0 || dp[il-1] >= n)
    cout << "Yes\n";
  else
    cout << "No\n";
}
