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

int main()
{
    int n, m, q;
    cin >> n >> m >> q;
    int aa[100005]{0};
    for(int i = 0; i < q; i++){
        cin >> aa[i];
        aa[i]--;
    }
    int b[100005]{0};
    int d[100005];
    int e[100005];
    int c = 0;
    vector<int> v[100005];
    for(int i = q - 1; i >= 0; i--){
        int a = aa[i];
        if(b[a] == 0){
            d[a] = c;
            e[c] = a;
            c++;
        }
        if(b[a] < n){
            if(d[a] == 0 || b[a] < b[e[d[a] - 1]]){
                v[b[a]].push_back(a);
                b[a]++;
            }
        }
    }
    bool f[100005]{0};
    for(int x : v[0]) f[x] = true;
    for(int i = 0; i < m; i++){
        if(!f[i]) v[0].push_back(i);
    }
    fill(f, f + m, false);
    for(int x : v[n - 1]) f[x] = true;
    for(int i = 0; i < m; i++){
        if(!f[i]) v[n - 1].push_back(i);
    }
    if(v[0] == v[n - 1]) cout << "Yes" << endl;
    else cout << "No" << endl;
}
