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 <cstdlib>
#include <algorithm>
#include <string>
#include <vector>
#include <cassert>

const int N = 1e5 + 7;

int n, m, q;
int a[N];
int visit[N], b[N];
std::vector<int> queue[N];

int main() {
	scanf("%d %d %d", &n, &m, &q);
	for (int i = 1; i <= q; i++) {
		scanf("%d", &a[i]);
	}
	for (int i = 1; i <= n; i++) {
		queue[0].push_back(i);
	}
	for (int i = 1; i <= m; i++) {
		visit[i] = -1;
	}
	int cur = 0;
	for (int i = q; i >= 1; i--) {
		int num = a[i];
		if (visit[num] != -1) {
			int pos = visit[num];
			if (queue[pos - 1].size()) {
				int back = queue[pos - 1].back();
				queue[pos - 1].pop_back();
				queue[pos].push_back(back);
			}
		} else {
			visit[num] = ++cur;
			assert(queue[cur - 1].size());
			int back = queue[cur - 1].back();
			queue[cur - 1].pop_back();
			b[cur] = num;
			queue[cur].push_back(back);
		}
	}
	for (int i = cur + 1, ptr = 1; i <= m; i++) {
		while (visit[ptr] != -1) {
			ptr++;
		}
		b[i] = ptr;
		visit[ptr] = i;
	}
	/*
	printf("b = \n");
	for (int i = 1; i <= m; i++) {
		printf("%d ", b[i]);
	}
	puts("");
	*/
	int least = cur;
	for (int i = 0; i <= cur; i++) {
		if (queue[i].size()) {
			least = i;
			break;
		}
	}
	//printf("%d\n", least);
	for (int i = least + 1; i < m; i++) {
		if (b[i] > b[i + 1]) {
			puts("No");
			return 0;
		}
	}
	puts("Yes");
	return 0;
}
