#include <bits/stdc++.h>
using namespace std;

constexpr int INF = 1<<30;

int main(){
    int n, k;
    while(cin >> n >> k, n){
        vector<int> v;
        int m = 0;
        for(int i=0;i<k;i++){
            int a;
            cin >> a;
            if(a != 0) v.push_back(a);
            else m++;
        }
        n = v.size();
        sort(v.begin(),v.end());
        v.push_back(INF);
        int ans = 0;
        for(int l=0,r=0,c=0;r<n;){
            while(c<=m && r<n){
                c += v[r+1]-v[r]-1;
                r++;
                if(c<=m) ans = max(ans, v[r]-v[l]+1);
            }
            while(c>m && l<=r){
                c -= v[l+1]-v[l]-1;
                l++;
                if(c<=m) ans = max(ans, v[r]-v[l]);
            }
        }
        cout << ans << endl;
    }
    return 0;
}


### Prompt

Please provide a Cpp coded solution to the problem described below:

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 <bits/stdc++.h>
using namespace std;

constexpr int INF = 1<<30;

int main(){
    int n, k;
    while(cin >> n >> k, n){
        vector<int> v;
        int m = 0;
        for(int i=0;i<k;i++){
            int a;
            cin >> a;
            if(a != 0) v.push_back(a);
            else m++;
        }
        n = v.size();
        sort(v.begin(),v.end());
        v.push_back(INF);
        int ans = 0;
        for(int l=0,r=0,c=0;r<n;){
            while(c<=m && r<n){
                c += v[r+1]-v[r]-1;
                r++;
                if(c<=m) ans = max(ans, v[r]-v[l]+1);
            }
            while(c>m && l<=r){
                c -= v[l+1]-v[l]-1;
                l++;
                if(c<=m) ans = max(ans, v[r]-v[l]);
            }
        }
        cout << ans << endl;
    }
    return 0;
}


```