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 main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N,M,Q; cin >> N >> M >> Q;
    vector<int> a(Q);
    for (int i=0;i<Q;++i) cin >> a[i],--a[i];
    reverse(a.begin(),a.end());
    vector<vector<int>> v(N);
    vector<int> nxt(M,0),idx(M,-1);
    for (int i=0;i<Q;++i){
        if (~idx[a[i]]){
            if (nxt[a[i]]>=N||v[nxt[a[i]]].size()<idx[a[i]]) continue;
            v[nxt[a[i]]++].emplace_back(a[i]);
        } else {
            idx[a[i]]=v[0].size();
            v[nxt[a[i]]++].emplace_back(a[i]);
        }
    }
    vector<int> check(M,0);
    for (int i=0;i<v[N-1].size();++i) check[v[N-1][i]]=1;
    for (int i=0;i<M;++i) if (!check[i]){
        v[N-1].emplace_back(i);
    }
    for (int i=0;i<N-1;++i){
        for (int j=0;j<v[i].size();++j){
            if (v[i][j]!=v[N-1][j]){
                cout << "No" << '\n';
                return 0;
            }
        }
    }
    cout << "Yes" << '\n';
}