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 smlst, N, M, Q, nr, b[100009], a[100009], pos[100009], need[100009];
bool ap[100009];

void Ans (bool x)
{
    if (x) printf ("Yes\n");
    else printf ("No\n");
    exit (0);
}

int main ()
{
//freopen ("input", "r", stdin);
//freopen ("output", "w", stdout);

scanf ("%d %d %d", &N, &M, &Q);
for (int i=1; i<=Q; i++)
    scanf ("%d", &a[i]);
b[++nr] = a[Q --], pos[b[1]] = 1;
need[1] = N - 1;
while (Q)
{
    int val = a[Q --];
    if (pos[val] != 0)
    {
        int p = pos[val];
        if (need[p]) need[p] --, need[p + 1] ++;
        continue;
    }
    b[++nr] = val, pos[val] = nr;
}
smlst = -1;
for (int i=1; i<=nr; i++)
    if (need[i] > 0)
    {
        smlst = i - 1;
        break;
    }
if (smlst == -1) Ans (1);
for (int i=1; i<=smlst; i++)
    ap[b[i]] = 1;
int j = smlst + 1;
for (int i=1; i<=M; i++)
    if (ap[i] == 0)
    {
        if (j > nr) break;
        if (i != b[j ++]) Ans (0);
    }
Ans (1);
return 0;
}
