#include <iostream>
using namespace std;
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <algorithm>
#include <functional> //sort(A,A.end(),greater<int>());???????????????
#include <queue>
#include <stack>
#include <vector>

#define INF 10 << 10

int card[100001];

int main() {
	int n, k;
	while (cin >> n >> k && n != 0 && k != 0) {

		memset(card, 0, sizeof(card));

		for (int i = 0; i < k; ++i) {
			int num;
			cin >> num;
			card[num] = 1;
		}

		int start = 1;
		int cnt = 0;
		int ans = 0;
		for (int i = 1; i <= n + 1; ++i) {
			if (card[i] == 0) {
				for (int i2 = start; i2 < i; ++i2) {
					card[i2] = cnt;
				}
				ans = max(ans, cnt);
				cnt = 0;
				start = i + 1;
			}
			else {
				cnt++;
			}
		}

		if (card[0] == 1) {
			for (int i = 1; i <= n; ++i) {
				if (card[i] == 0) {
					ans = max(ans, card[i - 1] + card[i + 1] + 1);
				}
			}
		}

		cout << ans << endl;
	}

	return 0;
}
### 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>
using namespace std;
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <algorithm>
#include <functional> //sort(A,A.end(),greater<int>());???????????????
#include <queue>
#include <stack>
#include <vector>

#define INF 10 << 10

int card[100001];

int main() {
	int n, k;
	while (cin >> n >> k && n != 0 && k != 0) {

		memset(card, 0, sizeof(card));

		for (int i = 0; i < k; ++i) {
			int num;
			cin >> num;
			card[num] = 1;
		}

		int start = 1;
		int cnt = 0;
		int ans = 0;
		for (int i = 1; i <= n + 1; ++i) {
			if (card[i] == 0) {
				for (int i2 = start; i2 < i; ++i2) {
					card[i2] = cnt;
				}
				ans = max(ans, cnt);
				cnt = 0;
				start = i + 1;
			}
			else {
				cnt++;
			}
		}

		if (card[0] == 1) {
			for (int i = 1; i <= n; ++i) {
				if (card[i] == 0) {
					ans = max(ans, card[i - 1] + card[i + 1] + 1);
				}
			}
		}

		cout << ans << endl;
	}

	return 0;
}
```