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>
#include <string>
#include <cmath>
#include <algorithm>
#include <utility>
#include <queue>
#include <set>
#include <map>
#include <deque>
#include <iomanip>
#include <cstdio>
#include <stack>
#include <numeric>

using namespace std;
typedef  long long ll;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<VI> VVI;
#define  MP make_pair
#define  PB push_back
#define inf 1000000007
#define mod 1000000007
#define rep(i,n) for(int i=0;i<(int)(n);++i)


int main(){
    int n,m;
    cin >> n >> m;
    int q;
    cin >> q;
    vector<int>a(q);
    vector<vector<int> > v(m+1);
    rep(i,q){
        cin >> a[i];
    }
    reverse(a.begin(),a.end());
    rep(i,q){
        v[a[i]].push_back(i);
    }
    rep(i,m+1){
        v[i].push_back(q);
    }
    vector<int>b(n,-1);
    vector<int>flag(m+1);
    int s = 1;
    bool f = 0;
    bool ok = 1;
    for(int i=0;i<q;i++){
        if(f){
            int k = a[i];
            if(flag[k])continue;
            for(int i=s;i<=m;i++){
                if(!flag[i]){
                    s = i;
                    break;
                }
            }
            if(s!=k){
                // cerr << s << " " << k << endl;
                // cerr << "Test" << endl;
                ok = 0;
            }
            flag[k] = true;
        }else{
            int k = a[i];
            if(flag[k]){
                continue;
            }
            int id = i-1;
            rep(zz,n){
                int t = *lower_bound(v[k].begin(),v[k].end(),max(id+1,b[zz]+1));
                //cerr << zz << " " << t << endl;
                if(t!=q){
                    b[zz] = t;
                    id = t;
                }else{
                    f = 1;
                    break;
                }
            }
            if(f){
                for(int i=s;i<=m;i++){
                    if(!flag[i]){
                        s = i;
                        break;
                    }
                }
                if(s!=k){
                    ok = 0;
                }

            }
            flag[k] = 1;
        }
    }
    if(ok){
        cout << "Yes" << endl;
    }else{
        cout << "No" << endl;
    }
    return 0;
}