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;

bool solve(const int N, const int M, vector<int> operations)
{
    auto stage_counts = vector<int>(M+1);
    stage_counts[0] = N;

    auto stage_labels = vector<int>(M);
    auto stages = vector<int>(M, -1);
    auto max_stage = 0;

    reverse(begin(operations), end(operations));

    for (const auto op : operations)
    {
        if (stages[op] == -1)
        {
            stages[op] = max_stage;
            stage_labels[max_stage] = op;
            max_stage++;
        }

        const auto s = stages[op];
        if (stage_counts[s] != 0)
        {
            stage_counts[s]--;
            stage_counts[s+1]++;
        }
    }

    auto permutation = vector<int>();
    auto used = vector<bool>(M);
    for (auto i = 0; i < M; i++)
    {
        if (stage_counts[i] != 0)
        {
            for (auto j = 0; j < M; j++) if (!used[j])
                permutation.push_back(j);
            break;
        }
        permutation.push_back(stage_labels[i]);
        used[stage_labels[i]] = true;
    }

    for (auto i = 0; i < max_stage; i++)
        if (permutation[i] != stage_labels[i]) return false;
    return true;
}

int main()
{
    int N, M; cin >> N >> M;

    int Q; cin >> Q;

    auto operations = vector<int>(Q);
    for (auto& x : operations)
    {
        cin >> x;
        x--;
    }

    cout << (solve(N, M, move(operations)) ? "Yes" : "No") << endl;
}
