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 <sstream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <algorithm>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <functional>
#include <complex>
#include <bitset>
#include <numeric>
using namespace std;

typedef long long LL;
#define REP(i,n) for(int (i)=0; (i)<(n) ;++(i))
#define REPN(i,a,n) FOR((i),(a),(a)+(n))
#define FOR(i,a,b) for(int (i)=(a); (i)<(b) ;++(i))
#define PB push_back
#define MP make_pair
#define OUT(a) cout<<(a)<<endl;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n,m,q,a[100010],rank[100010]={},cnt=1,l=0,dat[100010]={100010};
    vector<int> res;
    cin >> n >> m >> q;
    REP(i,q){
        cin >> a[i];
    }
    for(int i= q-1; i>=0;--i){
        if(rank[a[i]]==0){
            rank[a[i]]=cnt;
            ++cnt;
            res.push_back(a[i]);
        }
    }
    REPN(i,1,m){
        if(rank[i]==0){
            rank[i]=cnt;
            ++cnt;
            res.push_back(i);
        }
    }
    //OUT(l)
    for(int i=m-1;i>0;--i){
        if(res[i]<res[i-1]){
            l=i;
            break;
        }
    }

    for(int i= q-1; i>=0;--i){
        if(dat[rank[a[i]]]<dat[rank[a[i]]-1]){
        ++dat[rank[a[i]]];
        }
    }
    /*if(l==0){
        cout << "AAA" <<endl;
        return 0;
    }*/
    REPN(i,1,l){
        if(dat[i]<n){
            cout << "No" <<endl;
            return 0;
        }
    }
    cout << "Yes" <<endl;
    /*
    OUT(l)
    REP(i,m){
        OUT(res[i])
    }
    REP(i,m+1){
        OUT(dat[i])
    }
    //*/



    return 0;
}
