#include <iostream>
#include<cstdlib>
#include<queue>
#include<set>
#include<vector>
#include<string>
#include<algorithm>
#include<stack>
#include<map>
#include<cstdio>
#include<fstream>
using namespace std;
#define rep(i,a) for(int i=0;i<a;i++)

#define mp make_pair
#define P pair<int,int>
#define ll __int64
int n,k;
int t[111111];
int cnt[111111];
int dp[111111];
int kouho[111111];

int main(){

	while(cin>>n>>k,n||k){
	rep(i,110000)t[i]=cnt[i]=dp[i]=kouho[i]=0;
	rep(i,k)cin>>t[i];
	rep(i,k)cnt[t[i]]=1;
	
	int now=0,pos=0;

	for(int i=1;i<=n;i++){

		if(cnt[i]==1){
			now++;
			dp[i]=now;
		}

		else if(cnt[i]==0){
			now=0;
			kouho[pos++]=i;
		}
	}
	
	for(int i=n-1;i>=0;i--){
		if(dp[i]==0)now=0;

		if(now!=0)dp[i]=now;
		else if(dp[i]!=0){
			now=dp[i];
		}

	}
	int ans=0;

	if(cnt[0]==0){
		rep(i,n)ans=max(ans,dp[i]);
	}
	else{
		int x;
		for(int i=0;i<pos;i++){
			x=kouho[i];
			
			ans=max(ans,dp[x-1]+dp[x+1]+1);
		}
		//cout<<endl;
	}
	//rep(i,n+1)cout<<dp[i]<<" ";cout<<endl;
	cout<<ans<<endl;
	}
	return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

problem

There are n cards with one integer from 1 to n and one blank card. Of these n + 1 cards, k cards are given, but 1 ≤ k ≤ n. You can write one integer from 1 to n on a blank card. I want to make a continuous sequence of integers as long as possible with just a given card.

Write a program that outputs the maximum length of a contiguous sequence of integers that can be made from a given card when the given card is entered.



input

The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.

On the first line, two integers n (1 ≤ n ≤ 100000) and k (1 ≤ k ≤ n) are written in this order, separated by one blank. The following k line contains one integer. Written one by one, representing the integers written on the given k cards. Blank cards are represented by 0.

Of the scoring data, 40% of the points are 1 ≤ n ≤ 1000, 1 ≤ k ≤ 500, 20% of the points are 1 ≤ n ≤ 60000, 1 ≤ k ≤ 50000. Satisfy 1 ≤ n ≤ 100000, 1 ≤ k ≤ 100000.

The number of datasets does not exceed 5.

output

Outputs an integer on one line for each dataset.

Examples

Input

7 5
6
2
4
7
1
7 5
6
2
0
4
7
0 0


Output

2
4


Input

None


Output

None

### Response

```cpp
#include <iostream>
#include<cstdlib>
#include<queue>
#include<set>
#include<vector>
#include<string>
#include<algorithm>
#include<stack>
#include<map>
#include<cstdio>
#include<fstream>
using namespace std;
#define rep(i,a) for(int i=0;i<a;i++)

#define mp make_pair
#define P pair<int,int>
#define ll __int64
int n,k;
int t[111111];
int cnt[111111];
int dp[111111];
int kouho[111111];

int main(){

	while(cin>>n>>k,n||k){
	rep(i,110000)t[i]=cnt[i]=dp[i]=kouho[i]=0;
	rep(i,k)cin>>t[i];
	rep(i,k)cnt[t[i]]=1;
	
	int now=0,pos=0;

	for(int i=1;i<=n;i++){

		if(cnt[i]==1){
			now++;
			dp[i]=now;
		}

		else if(cnt[i]==0){
			now=0;
			kouho[pos++]=i;
		}
	}
	
	for(int i=n-1;i>=0;i--){
		if(dp[i]==0)now=0;

		if(now!=0)dp[i]=now;
		else if(dp[i]!=0){
			now=dp[i];
		}

	}
	int ans=0;

	if(cnt[0]==0){
		rep(i,n)ans=max(ans,dp[i]);
	}
	else{
		int x;
		for(int i=0;i<pos;i++){
			x=kouho[i];
			
			ans=max(ans,dp[x-1]+dp[x+1]+1);
		}
		//cout<<endl;
	}
	//rep(i,n+1)cout<<dp[i]<<" ";cout<<endl;
	cout<<ans<<endl;
	}
	return 0;
}

```