#include <bits/stdc++.h>

using namespace std;

#define int long long
#define PB push_back
#define BP while(1){}
typedef pair<int, int> pii;
static const int INF = 1LL<<61;

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int n, k;
  while (cin >> n >> k, n) {
    bool c[100005] = {false};
    for (int i = 0; i < k; ++i) {
      int t;
      cin >> t;
      c[t] = true;
    }

    int ans = 0, number[100005] = {0}, sum = 0;
    bool flg = false;
    for (int i = 1; i <= n; ++i) {
      if (!c[i]) continue;
      number[i] += 1 + number[i - 1];
    }

    for (int i = 1; i <= n; ++i) {
      if (c[i]) {
        sum++;
      } else if (!flg && c[0]) {
        flg = true;
        sum++;
      } else {
        flg = true;
        ans = max(ans, sum);
        if (c[0]) {
          sum = number[i - 1] + 1;
        } else
          sum = 0;
      }
    }

    cout << max(ans, sum) << endl;
  }

  return 0;
}
### Prompt

Your task is to create 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;

#define int long long
#define PB push_back
#define BP while(1){}
typedef pair<int, int> pii;
static const int INF = 1LL<<61;

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int n, k;
  while (cin >> n >> k, n) {
    bool c[100005] = {false};
    for (int i = 0; i < k; ++i) {
      int t;
      cin >> t;
      c[t] = true;
    }

    int ans = 0, number[100005] = {0}, sum = 0;
    bool flg = false;
    for (int i = 1; i <= n; ++i) {
      if (!c[i]) continue;
      number[i] += 1 + number[i - 1];
    }

    for (int i = 1; i <= n; ++i) {
      if (c[i]) {
        sum++;
      } else if (!flg && c[0]) {
        flg = true;
        sum++;
      } else {
        flg = true;
        ans = max(ans, sum);
        if (c[0]) {
          sum = number[i - 1] + 1;
        } else
          sum = 0;
      }
    }

    cout << max(ans, sum) << endl;
  }

  return 0;
}
```