#include <bits/stdc++.h>

using namespace std;

int main()
{
    int N, K;
    while (cin >> N >> K, N) {
        vector<int> a(N + 2, 0);
        vector<int> b(N + 2, 0);
        int x;
        bool white = 0;

        for (int i = 0; i < K; i++) {
            cin >> x;
            if (x == 0) {
                white = 1;
                continue;
            }
            a[x] = b[x] = 1;
        }
        for (int i = 1; i <= N; i++) {
            if (a[i] != 0) {
                a[i] += a[i-1];
            }
        }
        for (int i = N; i >= 1; i--) {
            if (b[i] != 0) {            
                b[i] += b[i+1];
            }
        }
        
        int res = 0;
        for (int i = 1; i <= N; i++) {            
            res = max(res, a[i]);
            if (white) {
                res = max(res, a[i-1] + b[i+1] + 1);
            }
        }
        cout << res << 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 <bits/stdc++.h>

using namespace std;

int main()
{
    int N, K;
    while (cin >> N >> K, N) {
        vector<int> a(N + 2, 0);
        vector<int> b(N + 2, 0);
        int x;
        bool white = 0;

        for (int i = 0; i < K; i++) {
            cin >> x;
            if (x == 0) {
                white = 1;
                continue;
            }
            a[x] = b[x] = 1;
        }
        for (int i = 1; i <= N; i++) {
            if (a[i] != 0) {
                a[i] += a[i-1];
            }
        }
        for (int i = N; i >= 1; i--) {
            if (b[i] != 0) {            
                b[i] += b[i+1];
            }
        }
        
        int res = 0;
        for (int i = 1; i <= N; i++) {            
            res = max(res, a[i]);
            if (white) {
                res = max(res, a[i-1] + b[i+1] + 1);
            }
        }
        cout << res << endl;
    }
    return 0;
}
```