#include "bits/stdc++.h"

//#define int long long

using namespace std;
#define REP(i, s, n) for(signed i = (s); i < signed(n); i++)
#define rep(i, n) REP(i, 0, n)
#define all(co) co.begin(), co.end()

typedef pair<int, int> P;
typedef unsigned long long LL;

#ifdef int
const long long INF = 1ll << 61ll;
#else
const signed INF = 1 << 29;
#endif

template<typename T = int>
vector<vector<T>> vvector(int h, int w, T def = T()) { return move(vector<vector<T>>(h, vector<T>(w, def))); }


signed main() {

	int n, k;
	while (cin >> n >> k && n)
	{
		n++;
		vector<int> dp(n + 2);
		bool white = false;
		rep(i, k) {
			int x; cin >> x;
			if(x) dp[x] = 1;
			else white = true;
		}
		rep(i, n) if (dp[i + 1]) dp[i + 1] = dp[i + 1] + dp[i];
		rep(i, n) if (dp[n - i]) dp[n - i] = max(dp[n - i], dp[n - i + 1]);
		int ans = 0;
		rep(i, n - 1) ans = max(ans, (white && !dp[i + 1] ? dp[i] + dp[i + 1] + dp[i + 2] + 1 : dp[i + 1]));
		cout << ans << endl;
	}
	return 0;
}
### Prompt

Your task is to create 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"

//#define int long long

using namespace std;
#define REP(i, s, n) for(signed i = (s); i < signed(n); i++)
#define rep(i, n) REP(i, 0, n)
#define all(co) co.begin(), co.end()

typedef pair<int, int> P;
typedef unsigned long long LL;

#ifdef int
const long long INF = 1ll << 61ll;
#else
const signed INF = 1 << 29;
#endif

template<typename T = int>
vector<vector<T>> vvector(int h, int w, T def = T()) { return move(vector<vector<T>>(h, vector<T>(w, def))); }


signed main() {

	int n, k;
	while (cin >> n >> k && n)
	{
		n++;
		vector<int> dp(n + 2);
		bool white = false;
		rep(i, k) {
			int x; cin >> x;
			if(x) dp[x] = 1;
			else white = true;
		}
		rep(i, n) if (dp[i + 1]) dp[i + 1] = dp[i + 1] + dp[i];
		rep(i, n) if (dp[n - i]) dp[n - i] = max(dp[n - i], dp[n - i + 1]);
		int ans = 0;
		rep(i, n - 1) ans = max(ans, (white && !dp[i + 1] ? dp[i] + dp[i + 1] + dp[i + 2] + 1 : dp[i + 1]));
		cout << ans << endl;
	}
	return 0;
}
```