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<stdio.h>
#include<algorithm>
#include<vector>
using namespace std;
int n, m, Q, w[101000], pv[101000], CC, ord[101000], R[101000];
struct point{
    int t, num;
    bool operator<(const point &p)const{
        return t<p.t;
    }
}P[101000];
int main(){
    int i, pp = -1;
    scanf("%d%d%d",&n,&m,&Q);
    for(i=1;i<=m;i++)P[i].num=i,P[i].t=i;
    for(i=1;i<=Q;i++){
        scanf("%d",&w[i]);
        P[w[i]].t=-i;
    }
    sort(P+1,P+m+1);
    for(i=1;i<=m;i++)ord[P[i].num] = i;
    for(i=m;i>=2;i--){
        if(P[i].num < P[i-1].num)break;
    }
    pp = i;
    R[0] = n;
    for(i=Q;i>=1;i--){
        int t = ord[w[i]];
        if(R[t] < R[t-1])R[t]++;
    }
    for(i=1;i<pp;i++){
        if(R[i] < n){
            printf("No\n");
            return 0;
        }
    }
    printf("Yes\n");
}