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;

#define int long long

#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}

int N,M;
int Q;
int r[111111];
int num[111111];

signed main(){
    cin>>N>>M;
    cin>>Q;
    vint A(Q);rep(i,Q)cin>>A[i];

    memset(r,-1,sizeof(r));

    int n=0;
    for(int i=Q-1;i>=0;i--){
        int a=A[i]-1;
        if(r[a]==-1){
            r[a]=n;
            n++;
        }
        if(r[a]&&num[r[a]-1]<=num[r[a]]);
        else num[r[a]]++;
    }

    vint x(n);
    rep(i,M)if(r[i]!=-1)x[r[i]]=i;
    rep(i,M)if(r[i]==-1)x.pb(i);

    int k=n;
    rep(i,n)if(num[i]<N){
        k=i;
        break;
    }
    bool flag=true;
    for(int i=k;i+1<M;i++)if(x[i]>x[i+1])flag=false;
    if(flag)cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
}
