#include <bits/stdc++.h>

using namespace std;

int N, K;
int DpLen[2][100002];
bool Used[100001];

int solve() {
	int maxLen;

	for (int i = 1; i <= N; ++i) {
		if (!Used[i]) {
			continue;
		}
		DpLen[0][i] = DpLen[0][i - 1] + 1;
	}
	for (int i = N; i >= 1; --i) {
		if (!Used[i]) {
			continue;
		}
		DpLen[1][i] = DpLen[1][i + 1] + 1;
	}

	maxLen = 1;


	for (int i = 1; i <= N; ++i) {
		maxLen = max(maxLen, max(DpLen[0][i], DpLen[1][i]));
		if (!Used[0] || Used[i]) {
			continue;
		}
		maxLen = max(maxLen, DpLen[0][i - 1] + 1 + DpLen[1][i + 1]);
	}

	return maxLen;
}

int main() {
	int a;

	while (cin >> N >> K, N) {
		memset(DpLen, 0, sizeof(DpLen));
		memset(Used, false, sizeof(Used));
		for (int i = 0; i < K; ++i) {
			cin >> a;
			Used[a] = true;
		}
		cout << solve() << 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>

using namespace std;

int N, K;
int DpLen[2][100002];
bool Used[100001];

int solve() {
	int maxLen;

	for (int i = 1; i <= N; ++i) {
		if (!Used[i]) {
			continue;
		}
		DpLen[0][i] = DpLen[0][i - 1] + 1;
	}
	for (int i = N; i >= 1; --i) {
		if (!Used[i]) {
			continue;
		}
		DpLen[1][i] = DpLen[1][i + 1] + 1;
	}

	maxLen = 1;


	for (int i = 1; i <= N; ++i) {
		maxLen = max(maxLen, max(DpLen[0][i], DpLen[1][i]));
		if (!Used[0] || Used[i]) {
			continue;
		}
		maxLen = max(maxLen, DpLen[0][i - 1] + 1 + DpLen[1][i + 1]);
	}

	return maxLen;
}

int main() {
	int a;

	while (cin >> N >> K, N) {
		memset(DpLen, 0, sizeof(DpLen));
		memset(Used, false, sizeof(Used));
		for (int i = 0; i < K; ++i) {
			cin >> a;
			Used[a] = true;
		}
		cout << solve() << endl;
	}

	return 0;
}

```