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;

int N, M, Q;
int L;
int A[100000];
int B[100000];
int prog[100000];
int cnt[100001];

int main()
{
    memset(prog, -1, sizeof prog);
    memset(B, -1, sizeof B);
    scanf("%d%d%d", &N, &M, &Q);
    for(int i=0; i<Q; i++)
        scanf("%d", A+i), A[i]--;
    L=0;
    cnt[0]=N;
    for(int i=Q-1; i>=0; i--)
    {
        int x=A[i];
        if(prog[x]==-1)
        {
            B[L]=x;
            prog[x]=L++;
        }
        if(cnt[prog[x]]>0)
            cnt[prog[x]]--, cnt[prog[x]+1]++;
    }
    for(int i=0; i<M; i++) if(prog[i]==-1)
    {
        B[L]=i;
        prog[i]=L++;
    }
    int idx=0;
    for(int i=L-1; i>=1; i--)
    {
        if(B[i-1]>B[i])
        {
            idx=i;
            break;
        }
    }
    for(int i=0; i<idx; i++) if(cnt[i]>0)
    {
        printf("No\n");
        return 0;
    }
    printf("Yes\n");
    return 0;
}
