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 pair<int, int> pii;
typedef pair<ll, ll> pll;

const int N = 200 * 1000 + 10;

int a[N];
int cnt[N];

vector<int> work(int m, vector<int> action) {
    set<int> all;
    for (int a : action)
        all.insert(a);
    //reverse(action.begin(), action.end());
    vector<int> res = action;
    for (int i = 0; i < m; i++)
        if (all.find(i) == all.end())
            res.push_back(i);
    return res;
}

int main() {
    ios_base::sync_with_stdio(0);
    int n, m, q;
    cin >> n >> m >> q;
    vector<int> pref;
    map<int, int> pos;
    int last = 0;
    cnt[0] = n;
    for (int i = 0; i < q; i++) {
        cin >> a[i];
        a[i]--;
    }
    for (int i = q - 1; i >= 0; i--) {
        if (pos.find(a[i]) == pos.end()) {
            pos[a[i]] = pref.size();
            cnt[last]--;
            last++;
            cnt[last]++;
            pref.push_back(a[i]);
        } else {
            if (cnt[pos[a[i]]] > 0) {
                cnt[pos[a[i]]]--;
                cnt[pos[a[i]] + 1]++;
            }
        }
    }    
    int minP = last;
    for (int i = 0; i <= last; i++)
        if (cnt[i]) {
            minP = i;
            break;
        }
    vector<int> r1 = work(m, pref);
    pref.resize(minP);
    vector<int> r2 = work(m, pref);
    cout << (r1 == r2 ? "Yes" : "No") << endl;        
    return 0;
}
