#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;

int n, k, a, x[500000], dp[500000][2], chain, maxn;
bool hakushi, ok;
vector<int>p;

int main() {
	while (true) {
		hakushi = false;
		for (int i = 0; i < 500000; i++) { x[i] = 0; dp[i][0] = 0; dp[i][1] = 0; }
		cin >> n >> k;
		if (n == 0 && k == 0) { break; }
		for (int i = 0; i < k; i++) {
			cin >> a;
			if (a == 0) { hakushi = true; }
			else { x[a] = 1; }
		}
		if (hakushi == false) {
			chain = 0; maxn = 0;
			for (int i = 1; i <= n; i++) {
				if (x[i] == 1) {
					chain++;
				}
				else {
					maxn = max(maxn, chain);
					chain = 0;
				}
			}
		}

		else {
			maxn = 0;
			for (int i = 1; i <= n; i++) {
				if (x[i] == 1) {
					dp[i][0] = max(dp[i][0], dp[i - 1][0] + 1);
					dp[i][1] = max(dp[i][1], dp[i - 1][1] + 1);
				}
				else {
					dp[i][0] = 0;
					dp[i][1] = max(dp[i][1], dp[i - 1][0] + 1);
				}
			}
			for (int i = 1; i <= n; i++) { maxn = max(maxn, max(dp[i][0], dp[i][1])); }
		}

		cout << maxn << endl;
	}
	return 0;
}
### Prompt

Please create a solution in CPP 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<iostream>
#include<algorithm>
#include<vector>
using namespace std;

int n, k, a, x[500000], dp[500000][2], chain, maxn;
bool hakushi, ok;
vector<int>p;

int main() {
	while (true) {
		hakushi = false;
		for (int i = 0; i < 500000; i++) { x[i] = 0; dp[i][0] = 0; dp[i][1] = 0; }
		cin >> n >> k;
		if (n == 0 && k == 0) { break; }
		for (int i = 0; i < k; i++) {
			cin >> a;
			if (a == 0) { hakushi = true; }
			else { x[a] = 1; }
		}
		if (hakushi == false) {
			chain = 0; maxn = 0;
			for (int i = 1; i <= n; i++) {
				if (x[i] == 1) {
					chain++;
				}
				else {
					maxn = max(maxn, chain);
					chain = 0;
				}
			}
		}

		else {
			maxn = 0;
			for (int i = 1; i <= n; i++) {
				if (x[i] == 1) {
					dp[i][0] = max(dp[i][0], dp[i - 1][0] + 1);
					dp[i][1] = max(dp[i][1], dp[i - 1][1] + 1);
				}
				else {
					dp[i][0] = 0;
					dp[i][1] = max(dp[i][1], dp[i - 1][0] + 1);
				}
			}
			for (int i = 1; i <= n; i++) { maxn = max(maxn, max(dp[i][0], dp[i][1])); }
		}

		cout << maxn << endl;
	}
	return 0;
}
```