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 <iostream>
#include <fstream>
#include <sstream>
#include <iomanip> 
#include <complex> 
#include <string>
#include <vector> 
#include <list>
#include <deque> 
#include <stack> 
#include <queue> 
#include <set>
#include <map>
#include <bitset>
#include <functional>
#include <utility>
#include <algorithm> 
#include <numeric> 
#include <typeinfo> 
#include <cstdio>
#include <cstdlib> 
#include <cstring>
#include <cmath>
#include <climits> 
#include <ctime>
#define MOD 1000000007LL
using namespace std;
typedef long long ll;
typedef pair<int,int> P;

int n,m,q;
int a[100001];
vector<int> f;
vector<int> ff;
bool used[100001];
int place[100001];
int freq[100001];

int main(void){
	scanf("%d%d%d",&n,&m,&q);
	for(int i=0;i<q;i++){
		scanf("%d",&a[i]);
	}
	memset(used,false,sizeof(used));
	for(int i=q-1;i>=0;i--){
		if(!used[a[i]]){
			used[a[i]]=true;
			f.push_back(a[i]);
		}
	}
	for(int i=1;i<=m;i++){
		if(!used[i])f.push_back(i);
	}
	for(int i=0;i<m;i++){
		place[f[i]]=i;
	}
	freq[0]=n;
	for(int i=q-1;i>=0;i--){
		if(freq[place[a[i]]]>0){
			freq[place[a[i]]]--;
			freq[place[a[i]]+1]++;
		}
	}
	int mini=m;
	for(int i=m-1;i>=0;i--){
		if(freq[i]>0)mini=i;
	}
	memset(used,false,sizeof(used));
	for(int i=0;i<mini;i++){
		ff.push_back(f[i]);
		used[f[i]]=true;
	}
	for(int i=1;i<=m;i++){
		if(!used[i])ff.push_back(i);
	}
	bool flag=true;
	for(int i=mini;i<m;i++){
		if(f[i]!=ff[i])flag=false;
	}
	printf("%s\n",flag?"Yes":"No");
	return 0;
}