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 main(){
	int n, m; cin >> n >> m;
	vector<int> at(m, -1), cnt(m + 1, 0), stk;
	cnt[0] = n;
	int q; cin >> q;
	vector<int> op(q);
	for(int & v : op) cin >> v;
	reverse(op.begin(), op.end());
	for(int & v : op){
		v--;
		if(at[v] == -1){
			stk.push_back(v);
			at[v] = stk.size();
			cnt[at[v]] = 1;
		} else {
			if(cnt[at[v] - 1] > cnt[at[v]]){
				cnt[at[v]]++;
			}
		}
	}
	int len = stk.size() + 1;
	vector<int> res;
	for(int i = 0, j = 0; i < len; i = j){
		while(j < len && cnt[j] == cnt[i]) j++;
		vector<int> holm;
		for(int k = 1; k < j; k++) holm.push_back(stk[k - 1]);
		for(int k = 0; k < m; k++) if(at[k] == -1 || at[k] >= j) holm.push_back(k);
		if(res.empty()) res = holm;
		else if(res != holm){
			cout << "No" << endl;
			return 0;
		}
	}
	cout << "Yes" << endl;
	return 0;
}
