#define _CRT_SECURE_NO_WARNINGS

#include <stdio.h>
#include <math.h>
#include <vector>
#include <algorithm>
#include <functional>
#include <numeric>
#include <queue>
#include <string.h>

using namespace std;

#define rep(i,n) for (int i = 0; i < (n); i++)

int main() {

	for (;;) {
		int n, k, c[112345], a = 0;
		scanf("%d %d", &n, &k);
		if (!(n + k)) break;
		rep(i, k) scanf("%d", &c[i]);
		sort(c, c + k);
		if (c[0]) {
			int prev = -114514;
			int t = 1;
			rep(i, k) {
				if (c[i] == prev + 1) t++;
				else t = 1;
				prev = c[i];
				a = max(a, t);
			}
		}
		else {
			int prev = -114514;
			int t = 1;
			bool zero = false;
			rep(i, k) {
				if (c[i] == prev + 1) {
					t++;
					prev = c[i];
				}
				else if (!zero) {
					t++;
					zero = true;
					i--;
					prev = c[i] + 1;
				}
				else {
					t = 1;
					zero = false;
					prev = c[i];
				}
				a = max(a, t);
			}
		}
		printf("%d\n", a);
	}

	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
#define _CRT_SECURE_NO_WARNINGS

#include <stdio.h>
#include <math.h>
#include <vector>
#include <algorithm>
#include <functional>
#include <numeric>
#include <queue>
#include <string.h>

using namespace std;

#define rep(i,n) for (int i = 0; i < (n); i++)

int main() {

	for (;;) {
		int n, k, c[112345], a = 0;
		scanf("%d %d", &n, &k);
		if (!(n + k)) break;
		rep(i, k) scanf("%d", &c[i]);
		sort(c, c + k);
		if (c[0]) {
			int prev = -114514;
			int t = 1;
			rep(i, k) {
				if (c[i] == prev + 1) t++;
				else t = 1;
				prev = c[i];
				a = max(a, t);
			}
		}
		else {
			int prev = -114514;
			int t = 1;
			bool zero = false;
			rep(i, k) {
				if (c[i] == prev + 1) {
					t++;
					prev = c[i];
				}
				else if (!zero) {
					t++;
					zero = true;
					i--;
					prev = c[i] + 1;
				}
				else {
					t = 1;
					zero = false;
					prev = c[i];
				}
				a = max(a, t);
			}
		}
		printf("%d\n", a);
	}

	return 0;
}
```