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
#define _USE_MATH_DEFINES
#include <cassert>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <complex>
#include <cmath>
#include <numeric>
#include <bitset>
#include <functional>

using namespace std;

#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}

typedef long long int64;
typedef pair<int, int> ii;
const int INF = 1 << 29;
const int MOD = 1e9 + 7;

const int N = 1e5 + 10;
int a[N];
bool visit[N];

int main() {
  int n, m, q;
  scanf("%d%d%d", &n, &m, &q);
  for (int i = 0; i < q; ++i) {
    scanf("%d", &a[i]);
    --a[i];
  }
  vector<int> b, r(m);
  for (int i = q - 1; i >= 0; --i) {
    if (!visit[a[i]]) {
      b.push_back(a[i]);
      visit[a[i]] = true;
    }
  }
  for (int i = 0; i < m; ++i) {
    if (visit[i]) continue;
    b.push_back(i);
  }
  for (int i = 0; i < m; ++i) {
    r[b[i]] = i;
  }
  vector<int> freq(m + 1);
  freq[0] = n;
  for (int i = q - 1; i >= 0; --i) {
    int k = r[a[i]];
    if (freq[k]) {
      --freq[k];
      ++freq[k + 1];
    }
  }
  bool found = false;
  for (int i = 0; i < m; ++i) {
    if (freq[i]) {
      for (int j = i + 1; j < m; ++j) {
        if (b[j] < b[j - 1]) {
          found = true;
          break;
        }
      }
      break;
    }
  }
  puts(found ? "No" : "Yes");
  return 0;
}
