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 <set>
#include <cassert>
using namespace std;

const int N = 100500;
int wait[N];

int P[N];
int Q[N];
int A[N];

bool was[N];

int main() {
    int n, m, q;
    scanf("%d %d %d", &n, &m, &q);
    for (int i = 0; i < q; i++) {
        scanf("%d", &A[i]);
        --A[i];
    }
    int pt = 0;
    for (int i = q - 1; i >= 0; i--) {
        if (!was[A[i]])
            was[A[i]] = true, P[pt] = A[i], Q[A[i]] = pt, pt++;
    }
    set<int> unused;
    for (int i = 0; i <= m; i++)
        unused.insert(i);
    for (int i = 0; i < pt; i++)
        unused.erase(P[i]);
    while (pt > 0 && P[pt - 1] < *unused.begin()) {
        --pt;
        unused.insert(P[pt]);
    }

    wait[0] = n;
    for (int i = q - 1; i >= 0; i--) {
        int a = A[i];
        assert(was[a]);
        if (Q[a] >= pt)
            continue;
        if (wait[Q[a]])
            wait[Q[a]]--, wait[Q[a] + 1]++;
    }
    if (wait[pt] != n) {
        puts("No");
    } else {
        puts("Yes");
    }
}
