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 <cassert>
#include <vector>
#include <iostream>
using namespace std;

void ext(vector<int> &result, int len, int m, vector<int> &v) {
    vector<bool> used(m+1, false);
    for (int i = 0; i < len; i++) {
        int a = result[i];
        assert(!used[a]);
        v.push_back(a);
        used[a] = true;
    }
    for (int i = 1; i <= m; i++) if (!used[i]) v.push_back(i);
}

int main() {
    int n, m, q; cin >> n >> m >> q;
    int a[q];
    for (int i = 0; i < q; i++) cin >> a[i];
    vector<int> cnt(m+1, 0), len(n, 0), idx(m+1), result;
    for (int i = q-1; i >= 0; i--) {
        if (0 < cnt[a[i]]) {
            if (cnt[a[i]] < n && len[cnt[a[i]]] == idx[a[i]]) {
                len[cnt[a[i]]]++;
                cnt[a[i]]++;
            }
        } else {
            cnt[a[i]]++;
            len[0]++;
            idx[a[i]] = result.size();
            result.push_back(a[i]);
        }
        // cerr << "result = "; for (int x : result) cerr << x << " "; cerr << endl;
        // cerr << "length = "; for (int x : len) cerr << x << ' '; cerr << endl;
        // cerr << "idx = "; for (int x : idx) cerr << x << ' '; cerr << endl;
        // cerr << "cnt = "; for (int x : cnt) cerr << x << ' '; cerr << endl;
    }
    vector<int> v1, v2;
    ext(result, len[0], m, v1);
    ext(result, len[n-1], m, v2);
    for (int i = 0; i < m; i++) {
        // cerr << v1[i] << " " << v2[i] << endl;
        if (v1[i] != v2[i]) {
            cout << "No\n";
            return 0;
        }
    }
    cout << "Yes\n";
}
