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>

/* -------------------------------- Template -------------------------------- */

#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()

using namespace std;

using ll = long long;
using ld = long double;

template <typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template <typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }

template<typename T> T inf() { assert(false); }
template<> constexpr int inf<int>() { return 1e9; }
template<> constexpr ll inf<ll>() { return 1e18; }
template<> constexpr ld inf<ld>() { return 1e30; }

/* -------------------------------- Library -------------------------------- */

/* ---------------------------------- Main ---------------------------------- */

int main() {
  int N, M, Q;
  cin >> N >> M >> Q;
  vector<int> a(Q);
  for (int &i: a) { cin >> i; --i; }
  reverse(ALL(a));

  vector<int> ans;
  set<int> se;
  REP(i,M) se.insert(i);
  for (int i: a) {
    auto it = se.find(i);
    if (it != se.end()) {
      ans.push_back(*it);
      se.erase(it);
    }
  }
  for (int i: se) ans.push_back(i);
  int mi = 1e9;
  while (!ans.empty() && ans.back() < mi) {
    mi = ans.back(); ans.pop_back();
  }
  vector<int> it(M, -1);
  REP(i,ans.size()) it[ans[i]] = i;
  vector<int> res(ans.size(), 0);
  for (int i: a) {
    int id = it[i];
    if (id == -1) continue;
    // cout << id << " " << ans.size() << endl;
    if (id == 0 || res[id-1] > res[id]) ++res[id];
  }
  bool flag = (res.size() == 0 || res.back() >= N);
  cout << (flag ? "Yes" : "No") << endl;
  return 0;
}
