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;

#define MAX 100002

int n;
int m;
int q;

int a[MAX];

set<int> s;
deque<int> v;
bool can[MAX];

multiset<int> mp;
int id[MAX];

int main(){
	cin >> n >> m >> q;
	for (int i = 0; i < q; i++){
		scanf("%d", &a[i]);
	}
	reverse(a, a + q);
	for (int i = 0; i < q; i++){
		if (s.count(a[i])==0){
			v.push_back(a[i]);
			s.insert(a[i]);
		}
	}
	for (int i = 1; i <= m; i++){
		if (s.count(i) == 0){
			v.push_back(i);
		}
	}
	int maxx = INT_MAX;
	can[v.size()] = true;
	for (int i = v.size() - 1; i >= 0; i--){
		if (maxx > v[i]){
			maxx = v[i];
			can[i] = true;
		}
		else{
			break;
		}
	}
	s.clear();
	for (int i = 0; i < v.size(); i++){
		id[v[i]] = i;
	}
	for (int i = 0; i < n; i++){
		mp.insert(0);
	}
	int L = -1;
	for (int i = 0; i < q; i++){
		int ID = id[a[i]];
		if (mp.count(ID)){
			auto k = mp.find(ID);
			mp.erase(k);
			mp.insert(ID + 1);
			continue;
		}
		if (ID <= L){
			continue;
		}
		L = max(L, ID);
	}
	for (auto it = mp.begin(); it != mp.end(); it++){
		if (can[(*it)] == false){
			puts("No");
			return 0;
		}
	}
	puts("Yes");
	return 0;
}