#include<iostream>
#include<algorithm>
using namespace std;


int len[100001];
int a[100001];
int n,k;

int main(){
  for(;;){
    cin >> n >> k;
    if(!n && !k)break;
    for(int i=0;i<k;i++)cin >> a[i];
    for(int i=0;i<=n;i++)len[i] = 0;
    sort(a,a+k);

    int pos=0;
    int dif=1;

    if(!a[0])pos++;
    while(pos<k){
      while(pos+dif<k && a[pos+dif-1]+1==a[pos+dif])dif++;
      for(int i=0;i<dif;i++)len[a[pos]+i] = dif;
      pos += dif;
      dif = 1;
    }

    int m=0;
    if(a[0]){
      for(int i=0;i<=n;i++)m = max(m,len[i]);
    }else{
      for(int i=0;i<=n;i++)
	if(i && i!=n-1 && !len[i])m = max(m,len[i-1] + len[i+1] + 1);
    }
    cout << m << 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<algorithm>
using namespace std;


int len[100001];
int a[100001];
int n,k;

int main(){
  for(;;){
    cin >> n >> k;
    if(!n && !k)break;
    for(int i=0;i<k;i++)cin >> a[i];
    for(int i=0;i<=n;i++)len[i] = 0;
    sort(a,a+k);

    int pos=0;
    int dif=1;

    if(!a[0])pos++;
    while(pos<k){
      while(pos+dif<k && a[pos+dif-1]+1==a[pos+dif])dif++;
      for(int i=0;i<dif;i++)len[a[pos]+i] = dif;
      pos += dif;
      dif = 1;
    }

    int m=0;
    if(a[0]){
      for(int i=0;i<=n;i++)m = max(m,len[i]);
    }else{
      for(int i=0;i<=n;i++)
	if(i && i!=n-1 && !len[i])m = max(m,len[i-1] + len[i+1] + 1);
    }
    cout << m << endl;
  }
}
```