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 <bits/stdc++.h>

using namespace std;

int n, m, q;

vector<int> order;
int place[112123];
int ops[112123];
int seen[112123];

int main()
{
	fill(place, place + 112123, -1);
	cin >> n >> m >> q;
	for (int i = 0; i < q; i++)
	{
		cin >> ops[i];
	}
	for (int i = q-1; i >= 0; i--)
	{
		int x = ops[i];
		if (place[x] == -1)
		{
			place[x] = order.size();
			order.push_back(x);
		}
		if (place[x] == 0 || seen[order[place[x]-1]] > seen[x])
			seen[x]++;
	}
	bool good = true;
	for (int i = 1; i <= m; i++)
	{
		int x = i;
		if (place[x] == -1)
		{
			place[x] = order.size();
			order.push_back(x);
		}
		if (place[x] == 0)
			seen[x] = n;
		else if (seen[order[place[x]-1]] > seen[x])
			seen[x] = seen[order[place[x]-1]];
	}
	for (int i = 1; i <= m; i++)
		if (seen[i] < n) good = false;
	if (good) cout << "Yes\n";
	else cout << "No\n";
	return 0;
}

