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>
#define pb push_back
#define mp make_pair
#define int long long
#define inf 1000000007
#define LINF 1000000000000000007LL
#define ll long long
using namespace std;
int used[114514];
int inv[114514];
signed main(){
	int n,m,q;
	cin>>n>>m>>q;
	vector<int> a;
	for(int i=0;i<q;i++){
		int x; cin>>x; a.pb(x);
	}
	reverse( a.begin(), a.end() );
	vector<int> b;
	b = a;
	for(int i=1;i<=m;i++){
		b.pb(i);
	}
	vector<int> c;
	for(int i=0;i<b.size();i++){
		if( used[b[i]]==0 ){ c.pb(b[i]); used[b[i]] = 1;}
	}
	for(int i=0;i<c.size();i++){ inv[ c[i] ] = i+1; }
	multiset<int> ms;
	for(int i=0;i<n;i++){
		ms.insert(0);
	}
	int goal = m;
	while( goal > 1 && c[goal-1] > c[goal-2] )goal--;
	goal--;
	multiset<int>::iterator it;
	for(int i=0;i<q;i++){
		int cur = inv [ a[i] ];
		it = ms.find(cur-1);
		if( it != ms.end() ){
			ms.erase( it );
			ms.insert( cur );
		}
		//cout<<"cur"<<cur<<" "; for(auto itr = ms.begin(); itr != ms.end(); ++itr)cout<<*itr<<" "; cout<<endl;
	}
	int cnt = 0;
	it = ms.begin();
	while( it != ms.end() ){
		//cout<<*it<<" ";
		if( *it >= goal ) cnt++;
		it++;
	}
	if( cnt == n )cout<<"Yes"<<endl;
	else cout<<"No"<<endl;
	return 0;
}