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 <string>
#include <vector>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <map>
#include <list>
#include <set>
#include <numeric>
#include <queue>
#include <stack>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <cstring>
#include <climits>
#include <cfloat>
#include <ctime>
#include <complex>
#include <cassert>
#include <array>
#include <bitset> 
#include <unordered_map>

using namespace std;
typedef long long LL;
typedef pair<int,int> P;

const int L=1e5+10;
vector<int> pos[L];
int lb[L];
bool done[L];
int main() {
	int N,M,Q;
	cin >> N >> M >> Q;
	vector<int> as;
	for(int i=0;i<Q;i++){
		int a;
		cin >> a;
		pos[a].push_back(Q-1-i);
		as.push_back(a);
	}
	for(int i=1;i<=M;i++){
		reverse(pos[i].begin(),pos[i].end());

	}
	for(int i=0;i<N;i++){
		lb[i]=i;
	}
	reverse(as.begin(),as.end());
	done[0]=true;
	int c=0;

	bool breaked=false;
	for(int i=0;i<Q;i++){
		int a=as[i];
		if(done[a])continue;
		done[a]=true;
		if(!breaked){
			for(int j=0;j<N;j++){
				auto it=lower_bound(pos[a].begin(),pos[a].end(),lb[j]);
				if(it==pos[a].end()){
					breaked=true;
					//cerr << "bbb " << i << ", " << j << ", " << lb[j] << ": " << a << endl;
					break;
				}
				//cerr << lb[j] << ", " << *it << endl;
				lb[j]=*it;
				lb[j+1]=max(lb[j+1],lb[j]+1);
			}
		}
		if(breaked){
			while(c<a){
				if(!done[c]){
					cout << "No" << endl;
					return 0;
				}
				c++;
			}
		}
	}

	cout << "Yes" << endl;


	return 0;
}

