#include <bits/stdc++.h>  

using namespace std;

#define FOR(i, j, k) for(int i = j; i < k; ++i)
#define rep(i, j) FOR(i, 0, j)
#define repr(i, j) for(int i = j; i >= 0; --i)
#define INF (1 << 30)
#define MOD 1e9 + 7

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> P;

int N, K;
bool card[100010];

int main() {
	while(scanf("%d %d", &N, &K), N || K) {
		memset(card, false, sizeof(card));
		bool unknown = false;
		rep(i, K) {
			int c;
			scanf("%d", &c);
			if(c == 0) {
				unknown = true;
				continue;
			}
			card[c] = true;
		}
		bool flag = false;
		int cnt = 0, now, prev = 0, mini = 0;
		int ans = 0;
		FOR(i, 1, N + 1) {
			if(card[i]) {
				if(i == mini + 2) flag = true;
				++cnt;
			}
			else {
				now = cnt;
				if(unknown && flag) {
					ans = max(ans, prev + now + 1);
				}
				else ans = max(ans, now);
				cnt = 0;
				flag = false;
				prev = now;
				mini = i;
			}
		}
		printf("%d\n", ans);
	}
	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>  

using namespace std;

#define FOR(i, j, k) for(int i = j; i < k; ++i)
#define rep(i, j) FOR(i, 0, j)
#define repr(i, j) for(int i = j; i >= 0; --i)
#define INF (1 << 30)
#define MOD 1e9 + 7

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> P;

int N, K;
bool card[100010];

int main() {
	while(scanf("%d %d", &N, &K), N || K) {
		memset(card, false, sizeof(card));
		bool unknown = false;
		rep(i, K) {
			int c;
			scanf("%d", &c);
			if(c == 0) {
				unknown = true;
				continue;
			}
			card[c] = true;
		}
		bool flag = false;
		int cnt = 0, now, prev = 0, mini = 0;
		int ans = 0;
		FOR(i, 1, N + 1) {
			if(card[i]) {
				if(i == mini + 2) flag = true;
				++cnt;
			}
			else {
				now = cnt;
				if(unknown && flag) {
					ans = max(ans, prev + now + 1);
				}
				else ans = max(ans, now);
				cnt = 0;
				flag = false;
				prev = now;
				mini = i;
			}
		}
		printf("%d\n", ans);
	}
	return 0;
}
```