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>
#pragma warning(disable : 4996)
int N, M, Q, a[100009], c[100009], p[100009], inv[100009];
int main() {
	scanf("%d%d%d", &N, &M, &Q);
	for (int i = 0; i < Q; i++) scanf("%d", &a[i]), a[i]--;
	for (int i = 0; i < M; i++) inv[i] = -1;
	int cur = 0;
	for (int i = Q - 1; i >= 0; i--) {
		if (inv[a[i]] == -1) {
			inv[a[i]] = cur;
			c[cur] = 1;
			p[cur++] = a[i];
		}
		else {
			if (c[inv[a[i]]] < (inv[a[i]] == 0 ? N : c[inv[a[i]] - 1])) {
				c[inv[a[i]]]++;
			}
		}
	}
	for (int i = 0; i < M; i++) {
		if (inv[i] == -1) p[cur++] = i;
	}
	bool ret = true;
	for (int i = 0; i < M; i++) {
		if (i >= 1 && c[i - 1] != N && p[i - 1] > p[i]) {
			ret = false;
		}
	}
	printf(ret ? "Yes\n" : "No\n");
	return 0;
}