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 <cstdio>
#include <algorithm>

using namespace std;

int v[100010], ap[100010], nr[100010], a[100010];

int main ()
{
   // freopen ("file.in", "r", stdin);

    int n, m, q;
    scanf ("%d %d %d", &n, &m, &q);

    nr[0] = n;
    for (int i = 1; i <= q; ++i)
        scanf ("%d", &v[q - i + 1]);

    int k = 0;
    for (int i = 1; i <= q; ++i)
        if (!ap[v[i]]) ap[a[++k] = v[i]] = k;

    for (int i = 1; i <= m; ++i)
        if (!ap[i]) ap[a[++k] = i] = k;

    for (int i = 1; i <= q; ++i)
    {
        int fr = ap[v[i]];
        if (nr[fr - 1] > 0) --nr[fr - 1], ++nr[fr];
    }

    for (int i = 0; i < m; ++i)
        if (nr[i] > 0)
        {
            for (++++i; i <= m; ++i)
                if (a[i] < a[i - 1])
                {
                    printf ("No\n");
                    return 0;
                }

            break;
        }

    printf ("Yes\n");

    return 0;
}
