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> n_fixed(m+1, 0);
	n_fixed[0] = n;

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

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

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

			n_fixed[order.size()]++;
			n_fixed[order.size()-1]--;
// show(n_fixed, "n_fixed");
			continue;
		}

		int pos = num_pos[a[i]];
// printf("pos %d\n", pos);
		if (n_fixed[pos] > 0) {
			n_fixed[pos]--;
			n_fixed[pos+1]++;
		}
// show(n_fixed, "n_fixed");
	}

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

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

	auto it = find_if(n_fixed.begin(), n_fixed.end(),
	                  [](const int &a) {return a > 0;});
	int min_fix = it - n_fixed.begin();
// printf("min_fix %d\n", min_fix);

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

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