#include "bits/stdc++.h"
#define MOD 1000000007
#define INF 11234567890
#define in std::cin
#define out std::cout
#define rep(i,N) for(int i=0;i<N;++i)
typedef long long int LL;

int n, k, a[112345];
bool flag, tmp;
int res, ans;

int main()
{
	while (true)
	{
		memset(a, 0, sizeof(a));
		res = ans = 1;

		in >> n >> k;
		if (n == 0 && k == 0) { break; }
		rep(i, k) { in >> a[i]; }

		std::sort(a, a + k);
		tmp = flag = (a[0] == 0 ? true : false);
		rep(i, k - 1)
		{
			if (a[i] == 0) { continue; }
			if (a[i] + 1 == a[i + 1]) { ++res; }
			else if (a[i] + 2 == a[i + 1] && tmp)
			{
				res += 2;
				tmp = false;
			}
			else
			{
				ans = std::max(ans, res);
				res = 1;
				tmp = flag;
				if (a[i] + 1 == a[i + 1]) { ++res; }
				else if (a[i] + 2 == a[i + 1] && tmp)
				{
					res += 2;
					tmp = false;
				}
			}
		}
		out << std::max(ans, res) << std::endl;
	}
	return 0;
}
### Prompt

Generate 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"
#define MOD 1000000007
#define INF 11234567890
#define in std::cin
#define out std::cout
#define rep(i,N) for(int i=0;i<N;++i)
typedef long long int LL;

int n, k, a[112345];
bool flag, tmp;
int res, ans;

int main()
{
	while (true)
	{
		memset(a, 0, sizeof(a));
		res = ans = 1;

		in >> n >> k;
		if (n == 0 && k == 0) { break; }
		rep(i, k) { in >> a[i]; }

		std::sort(a, a + k);
		tmp = flag = (a[0] == 0 ? true : false);
		rep(i, k - 1)
		{
			if (a[i] == 0) { continue; }
			if (a[i] + 1 == a[i + 1]) { ++res; }
			else if (a[i] + 2 == a[i + 1] && tmp)
			{
				res += 2;
				tmp = false;
			}
			else
			{
				ans = std::max(ans, res);
				res = 1;
				tmp = flag;
				if (a[i] + 1 == a[i + 1]) { ++res; }
				else if (a[i] + 2 == a[i + 1] && tmp)
				{
					res += 2;
					tmp = false;
				}
			}
		}
		out << std::max(ans, res) << std::endl;
	}
	return 0;
}
```