#include<iostream>
#include<cmath>
#include<vector>
#include<string>
typedef unsigned long long ull;
#define rep(i,a) for(int i=0;i<a;i++)
#define loop(i,a,b) for(int i=a;i<b;i++)
using namespace std;
const double eps = 1e-10;
const double pi = acos(-1);
const double inf = (int)1e8;

int main(void){
  int n,k;
  while(cin>>n>>k,n+k){
    vector<bool> in(n+1,0);
    vector<bool> used;
    rep(i,k){
      int num;
      cin>>num;
      in[num]=true;
    }
    
    vector<int> dp(n);
    vector<int> box;
    int maxv = 0;
    loop(i,1,n+1){
      dp[i] = dp[i-1] + in[i];
      maxv = max(maxv,dp[i]);
      if(in[i]==0){
	dp[i] = 0;
	if(in[i-1] && in[i+1])box.push_back(i);
      }
    }
    if(in[0]){      
      for(int i = n-1 ; i > 0 ; i --){
	if(in[i])
	  dp[i] = max(dp[i],dp[i+1]);
      }
      rep(i,box.size()){
	maxv = max(maxv,dp[box[i]-1]+dp[box[i]+1]+1);
      }
    
    }
    cout<<maxv<<endl;
  }  
}
### Prompt

Create a solution in CPP for 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<cmath>
#include<vector>
#include<string>
typedef unsigned long long ull;
#define rep(i,a) for(int i=0;i<a;i++)
#define loop(i,a,b) for(int i=a;i<b;i++)
using namespace std;
const double eps = 1e-10;
const double pi = acos(-1);
const double inf = (int)1e8;

int main(void){
  int n,k;
  while(cin>>n>>k,n+k){
    vector<bool> in(n+1,0);
    vector<bool> used;
    rep(i,k){
      int num;
      cin>>num;
      in[num]=true;
    }
    
    vector<int> dp(n);
    vector<int> box;
    int maxv = 0;
    loop(i,1,n+1){
      dp[i] = dp[i-1] + in[i];
      maxv = max(maxv,dp[i]);
      if(in[i]==0){
	dp[i] = 0;
	if(in[i-1] && in[i+1])box.push_back(i);
      }
    }
    if(in[0]){      
      for(int i = n-1 ; i > 0 ; i --){
	if(in[i])
	  dp[i] = max(dp[i],dp[i+1]);
      }
      rep(i,box.size()){
	maxv = max(maxv,dp[box[i]-1]+dp[box[i]+1]+1);
      }
    
    }
    cout<<maxv<<endl;
  }  
}
```