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
#include <iostream>
#include <vector>
void solve(int n, int k) {
	if (n == 0 && k == 0) return;
	std::vector<int> dealed(n, 0);
	bool dealed_blank_card{ false };
	for (auto i = 0; i < k; ++i) {
		int card;
		std::cin >> card;
		if (card != 0) dealed[card - 1] = 1;
		else dealed_blank_card = true;
	}
	for (auto i = 1; i < n; ++i) {
		if (dealed[i] == 1) dealed[i] += dealed[i - 1];
	}
	for (auto i = n - 1; i > 0; --i) {
		if (dealed[i] > 0 && dealed[i - 1] > 0) dealed[i - 1] = dealed[i];
	}
	int max_length{ 0 };
	if (dealed_blank_card) {
		for (auto i = 0; i < n; ++i) {
			if (dealed[i] == 0) {
				int temp_length{ 0 };
				if (i > 0) temp_length += dealed[i - 1];
				if (i < n - 1) temp_length += dealed[i + 1];
				if (max_length <= temp_length) max_length = temp_length + 1;
			}
		}
	}
	else {
		for (auto i = 0; i < n; ++i) {
			if (max_length < dealed[i]) max_length = dealed[i];
		}
	}
	std::cout << max_length << std::endl;
	std::cin >> n >> k;
	solve(n, k);
}
int main() {
	int n, k;
	std::cin >> n >> k;
	solve(n, k);
}

