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;

typedef long long ll;
typedef long double ld;

const int M = 100100;

int n, m, q;
int a[M];
bool used[M];
int cnt[M];
int ord[M];
vector<int> seq;

void read() {
  cin >> n >> m >> q;
  for (int i = 0; i < q; ++i) {
    cin >> a[i];
    --a[i];
  }
  reverse(a, a + q);
}

void nx(int i) {
  assert(i < m);
  if (cnt[i] > 0) {
    --cnt[i];
    ++cnt[i + 1];
  }
}

void add(int x) {
  if (!used[x]) {
    int f = seq.size();

    used[x] = true;
    ord[x] = f;

    nx(f);
    seq.push_back(x);
  } else {
    int k = ord[x];
    nx(k);
  }
}

void kill() {
  cnt[0] = n;

  for (int i = 0; i < q; ++i)
    add(a[i]);

  for (int i = 0; i < m; ++i)
    if (!used[i])
      seq.push_back(i);

  int sh = 0;
  while (!cnt[sh])
    ++sh;
  
  auto alt = seq;
  sort(alt.begin() + sh, alt.end());

  if (alt == seq) {
    cout << "Yes\n";
  } else {
    cout << "No\n";
  }
}

int main() {
  cout.precision(20);
  cout << fixed;
  ios_base::sync_with_stdio(false);
  read();
  kill();
}
