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;

int main() {
   ios_base::sync_with_stdio(false); cin.tie(nullptr);
   int N, M; cin >> N >> M;
   vector<int> P(M, -1);
   vector<int> invP(M, -1);
   vector<int> freq(M+1);
   freq[0] = N;
   int Q; cin >> Q;
   vector<int> A(Q);
   for (int i = 0; i < Q; ++i) cin >> A[i], --A[i];
   int cur = 0;
   for (int i = Q-1; i >= 0; --i) {
      int z = A[i];
      if (invP[z] == -1) {
         P[cur] = z;
         invP[z] = cur;
         freq[cur]--;
         cur++;
         freq[cur]++;
         continue;
      }
      if (freq[invP[z]]) {
         freq[invP[z]]--;
         freq[invP[z]+1]++;
      }
   }
   for (int i = 0; i < M; ++i) if (invP[i] == -1) P[cur++] = i;
   cur = 0;
   while (freq[cur] == 0) cur++;
   if (is_sorted(P.begin()+cur, P.end())) {
      cout << "Yes\n";
   } else {
      cout << "No\n";
   }
   return 0;
}
