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<vector>
#include<cassert>
#include<algorithm>
using namespace std;
int n, m, q, a[100009], b[100009], c[100009], d[100009]; vector<int>Z; bool used[100009], OK;
int main() {
	cin >> n >> m >> q; for (int i = 0; i < m; i++)b[i] = -1;
	for (int i = 1; i <= q; i++)cin >> a[i], a[i]--;
	for (int i = q; i >= 1; i--) { if (used[a[i]] == false) { used[a[i]] = true; Z.push_back(a[i]); } }
	int E = 1e9; for (int i = 0; i < m; i++) { if (used[i] == false)E = min(E, i); }
	if (E > Z[Z.size() - 1]) {
		while (Z.size() >= 2 && Z[Z.size() - 2] < Z[Z.size() - 1])Z.pop_back();
		if (Z[Z.size() - 1] == 0)Z.pop_back();
	}
	for (int i = 0; i < Z.size(); i++)b[Z[i]] = i;
	if (Z.size() == 0) { cout << "Yes" << endl; return 0; }
	if (n*Z.size() > q) { cout << "No" << endl; return 0; }
	for (int i = q; i >= 1; i--) {
		int num = b[a[i]]; if (num == -1)continue;
		if (c[num] == n || d[c[num]] < num)continue;
		d[c[num]]++; c[num]++;
	}
	for (int i = 0; i < n; i++) { if (d[i] != Z.size())OK = true; }
	if (OK == true)cout << "No" << endl; else cout << "Yes" << endl;
	return 0;
}