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 <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <utility>
#include <map>

using namespace std;

void show(vector<int> &v, string s = "") {
	if (s.size() > 0) {
		cout << s << endl;
	}
	for (auto e : v) {
		cout << e << " ";
	}
	cout << endl;
}

int main() {
	int n, m, q;

	scanf("%d %d %d", &n, &m, &q);
	vector<int> a(q);
	for (int i = 0; i < q; i++) {
		scanf("%d", &a[i]);
		a[i]--;
	}

	reverse(a.begin(), a.end());

	vector<int> order;
	map<int, int> num_pos;
	vector<int> num_used(m, false);

	vector<int> fixed_index(n, 0);

	for (int i = 0; i < q; i++) {
// printf("a[%d] = %d\n", i, a[i]);
// show(fixed_index, "fixed_index");

		if (!num_used[a[i]]) {
			num_used[a[i]] = true;

			num_pos[a[i]] = order.size();
			order.emplace_back(a[i]);

			fixed_index.back()++;
			continue;
		}

		int pos = num_pos[a[i]];
// printf("pos %d\n", pos);
		auto it_bound = upper_bound(fixed_index.begin(), fixed_index.end(), pos);
		if (it_bound != fixed_index.begin()) {
			it_bound = prev(it_bound);
		}
// printf("it_bound %d\n", *it_bound);
		if (*it_bound == pos) {
			*it_bound += 1;
		}
	}

	// show(order, "order");
	// show(fixed_index, "fixed_index");

	for (int i = 0; i < m; i++) {
		if (!num_used[i]) {
			order.emplace_back(i);
		}
	}
	// show(order, "order");

	bool ok = true;
	for (int i = fixed_index[0]; i < order.size() - 1; i++) {
		if (order[i] > order[i+1]) {
			ok = false;
			break;
		}
	}

	cout << (ok ? "Yes" : "No") << endl;
	return 0;
}
