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;
vector<int> arr;
vector<int> chk;
vector<int> pnt;
vector<vector<int> > Pos;

int main() {
    scanf("%d %d %d", &N, &M, &Q);
    arr.resize(Q);
    Pos.resize(M);
    for(int i = 0; i < Q; i++) {
        scanf("%d", &arr[i]);
        arr[i]--;
        Pos[arr[i]].push_back(i);
    }
    chk = vector<int>(M, 0);
    pnt = vector<int>(N, Q);
    int mn = 0;
    int st = 0;
    for(int i = Q - 1; i >= 0; i--) {
        if(chk[arr[i]]) continue;
        while(mn < M && chk[mn]) mn++;
        bool ok = true;
        int pos = (int)Pos[arr[i]].size() - 1;
        for(int j = N - 1; j >= 0; j--) {
            while(pos >= 0 && Pos[arr[i]][pos] >= pnt[j]) pos--;
            if(pos < 0) {
                if(arr[i] != mn) ok = false;
                for(int k = j; k >= st; k--) pnt[k] = -1;
                st = j + 1;
                break;
            }
            pnt[j] = Pos[arr[i]][pos--];
        }
        if(!ok) {
            printf("No");
            return 0;
        }
        chk[arr[i]] = 1;
    }
    printf("Yes");
}
