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>

const int N = 100000;

int a[N], len[N], cnt[N], rnk[N];

int main()
{
  int n, m, q;
  while (scanf("%d%d%d", &n, &m, &q) == 3) {
    for (int i = 0; i < q; ++ i) {
      scanf("%d", a + i);
      a[i] --;
    }
    memset(len, 0, sizeof(*len) * n);
    memset(cnt, 0, sizeof(*cnt) * m);
    memset(rnk, -1, sizeof(*rnk) * m);
    std::vector<int> seq;
    for (int i = q - 1; i >= 0; -- i) {
      if (rnk[a[i]] == -1) {
        rnk[a[i]] = seq.size();
        seq.push_back(a[i]);
      }
      if (cnt[a[i]] < n && len[cnt[a[i]]] == rnk[a[i]]) {
        len[cnt[a[i]]] ++;
        cnt[a[i]] ++;
      }
    }
    int o = 0;
    while (o < m && ~rnk[o]) {
      o ++;
    }
    int min_len = seq.size();
    while (min_len && seq[min_len - 1] < o) {
      o = seq[-- min_len];
    }
    bool ok = true;
    for (int i = 0; i < n; ++ i) {
      ok &= len[i] >= min_len;
    }
    puts(ok ? "Yes" : "No");
  }
}
