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

int main() {
    int N, K;
    while (cin >> N >> K, N || K) {
        vector<int> v(N + 2);
        for (int i = 0; i < K; i++) {
            int x; cin >> x;
            v[x]++;
        }


        vector<pair<int,int> > d;
        int left;
        for (int i = 1, flag = false; i <= N; i++) {
            if (!flag && v[i]) left = i-1, flag = true;
            if (flag && !v[i]) d.push_back(pair<int,int>(left, i-1)), flag = false;
        }

        int ans = 0;
        for (int i = 0; i < (int)d.size(); i++) {
            if (!v[0]) ans = max(ans, d[i].second - d[i].first);
            else {
                ans = max(ans, d[i].second - d[i].first + 1);
                if (i + 1 < (int)d.size() && d[i].second + 1 == d[i+1].first) {
                    ans = max(ans,
                              d[i].second - d[i].first + 1
                              + d[i+1].second - d[i+1].first);
                }
            }
        }

        cout << ans << endl;

    }

    return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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;

int main() {
    int N, K;
    while (cin >> N >> K, N || K) {
        vector<int> v(N + 2);
        for (int i = 0; i < K; i++) {
            int x; cin >> x;
            v[x]++;
        }


        vector<pair<int,int> > d;
        int left;
        for (int i = 1, flag = false; i <= N; i++) {
            if (!flag && v[i]) left = i-1, flag = true;
            if (flag && !v[i]) d.push_back(pair<int,int>(left, i-1)), flag = false;
        }

        int ans = 0;
        for (int i = 0; i < (int)d.size(); i++) {
            if (!v[0]) ans = max(ans, d[i].second - d[i].first);
            else {
                ans = max(ans, d[i].second - d[i].first + 1);
                if (i + 1 < (int)d.size() && d[i].second + 1 == d[i+1].first) {
                    ans = max(ans,
                              d[i].second - d[i].first + 1
                              + d[i+1].second - d[i+1].first);
                }
            }
        }

        cout << ans << endl;

    }

    return 0;
}
```