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>

#define FO(i,a,b) for (int i = (a); i < (b); i++)
#define sz(v) int(v.size())

using namespace std;

int n, m, q;
int a[100005];
set<int> seen;
int v[100005];
int iv[100005];
int r;

int nw[100005];

int main() {
    scanf("%d %d %d", &n, &m, &q);
    FO(i,0,q) scanf("%d", a+i);
    reverse(a,a+q);
    FO(i,0,q) {
        if (!seen.count(a[i])) {
            seen.insert(a[i]);
            v[r++] = a[i];
        }
    }
    FO(i,1,m+1) if (!seen.count(i)) {
        v[r++] = i;
    }

    FO(i,0,m) {
        //printf("%d ", v[i]);
        iv[v[i]] = i;
    }
    //printf("\n");

    nw[0] = n;

    FO(i,0,q) {
        int o = iv[a[i]];
        if (nw[o]) {
            nw[o]--;
            nw[o+1]++;
        }
    }

    bool bd = false;
    for (int i = m-2; i >= 0; i--) {
        if (v[i] > v[i+1]) bd = true;
        if (bd && nw[i]) {
            printf("No\n");
            return 0;
        }
    }

    printf("Yes\n");
}

