#include <cstdio>
#include <algorithm>

using namespace std;

#define rep1(i,x) for(int i=1;i<=(x);++i)
#define chmax(a,b) a=max(a,b)

int a[100001];
int memo[100001];
int start[100001];

int main()
{
	int n, k;
	while (scanf("%d %d", &n, &k), n || k) {
		fill_n(a, n, 0);
		fill_n(memo, n, 0);
		fill_n(start, n, 0);

		bool f = false;

		rep1(i, k) {
			int tmp; scanf("%d", &tmp);
			if (tmp == 0) f = true;
			else a[tmp] = true;
		}

		rep1(i, n) {
			if (a[i]) {
				if (a[i - 1]) {
					start[i] = start[i - 1];
					memo[start[i]]++;
				} else {
					start[i] = i;
					memo[start[i]]++;
				}
			}
		}

		int ma = 0;

		rep1(i, n) {
			if (a[i]) {
				chmax(ma, memo[start[i]]);
			} else if (f) {
				if (i + 1 <= n) {
					chmax(ma, memo[start[i - 1]] + memo[start[i + 1]] + 1);
				} else {
					chmax(ma, memo[start[i - 1]] + 1);
				}
			}
		}

		printf("%d\n", ma);
	}
}
### Prompt

Please formulate 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 <cstdio>
#include <algorithm>

using namespace std;

#define rep1(i,x) for(int i=1;i<=(x);++i)
#define chmax(a,b) a=max(a,b)

int a[100001];
int memo[100001];
int start[100001];

int main()
{
	int n, k;
	while (scanf("%d %d", &n, &k), n || k) {
		fill_n(a, n, 0);
		fill_n(memo, n, 0);
		fill_n(start, n, 0);

		bool f = false;

		rep1(i, k) {
			int tmp; scanf("%d", &tmp);
			if (tmp == 0) f = true;
			else a[tmp] = true;
		}

		rep1(i, n) {
			if (a[i]) {
				if (a[i - 1]) {
					start[i] = start[i - 1];
					memo[start[i]]++;
				} else {
					start[i] = i;
					memo[start[i]]++;
				}
			}
		}

		int ma = 0;

		rep1(i, n) {
			if (a[i]) {
				chmax(ma, memo[start[i]]);
			} else if (f) {
				if (i + 1 <= n) {
					chmax(ma, memo[start[i - 1]] + memo[start[i + 1]] + 1);
				} else {
					chmax(ma, memo[start[i - 1]] + 1);
				}
			}
		}

		printf("%d\n", ma);
	}
}
```