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 const N = 1234567;
int a[N], used[N], d[N], ans[N];
set<pair<int, int> > f;
int cn;

void inc(int v) {
  f.erase({d[v], v});
  ++d[v];
  f.insert({d[v], v});
}

void add(int x) {
  used[x] = cn;
  ans[cn++] = x;
  inc(0);
}

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];
  }
  for (int i = 0; i < m; i++) used[i] = -1;
  cn = 0;
  for (int i = 0; i < n; i++) f.insert({0, i});
  for (int i = q - 1; i >= 0; i--) {
    if (used[a[i]] < 0) {
      add(a[i]);
      continue;
    }
    auto it = f.lower_bound({used[a[i]], -1});
    if (it == f.end() || it->first != used[a[i]]) {
      continue;
    }
    inc(it->second);
  }
  int mn = m;
  for (int i = 0; i < n; i++) {
    mn = std::min(mn, d[i]);
  }
  for (int i = 0; i < m; i++) {
    if (used[i] < 0) {
      add(i);
    }
  }
  for (int i = mn; i + 1 < m; i++) {
    if (ans[i] > ans[i + 1]) {
      puts("No");
      return 0;
    }
  }
  puts("Yes");
}
