#include<cstdio>
#include<algorithm>

using namespace std;

//n <= 100000
//k <= n

int dp[100003];

int main(void){
	int n,k;
	
	while(scanf("%d%d", &n, &k) && n && k){
		int temp;
		int ans=0;
		fill(dp,dp+100000,0);
		
		for(int i = 0; i < k; i++){
			scanf("%d", &temp);
			dp[temp] = 1;
		}
		
		for(int i = 2; i <= n; i++){
			if(dp[i] == 1)dp[i] = dp[i-1]+dp[i];
		}
		/*
		for(int i = 1; i <= n; i++){
			printf("%d ",dp[i]);
		}puts("");
		*/
		temp = 0;
		for(int i = n; i >= 1; i--){
			if(dp[i] == 0)temp = 0;
			else if(temp == 0)temp = dp[i];
			else dp[i] = temp;
		}
		/*
		for(int i = 1; i <= n; i++){
			printf("%d ",dp[i]);
		}puts("");
		*/
		
		if(dp[0]){
			for(int i = 1; i <= n; i++){
				if(dp[i] == 0){
					ans = max(dp[i-1]+dp[i+1]+1,ans);
				}
			}
		}
		else {
			for(int i = 1; i <= n; i++){
				ans = max(dp[i],ans);
			}
		}
		
		printf("%d\n", ans);
	}
	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<cstdio>
#include<algorithm>

using namespace std;

//n <= 100000
//k <= n

int dp[100003];

int main(void){
	int n,k;
	
	while(scanf("%d%d", &n, &k) && n && k){
		int temp;
		int ans=0;
		fill(dp,dp+100000,0);
		
		for(int i = 0; i < k; i++){
			scanf("%d", &temp);
			dp[temp] = 1;
		}
		
		for(int i = 2; i <= n; i++){
			if(dp[i] == 1)dp[i] = dp[i-1]+dp[i];
		}
		/*
		for(int i = 1; i <= n; i++){
			printf("%d ",dp[i]);
		}puts("");
		*/
		temp = 0;
		for(int i = n; i >= 1; i--){
			if(dp[i] == 0)temp = 0;
			else if(temp == 0)temp = dp[i];
			else dp[i] = temp;
		}
		/*
		for(int i = 1; i <= n; i++){
			printf("%d ",dp[i]);
		}puts("");
		*/
		
		if(dp[0]){
			for(int i = 1; i <= n; i++){
				if(dp[i] == 0){
					ans = max(dp[i-1]+dp[i+1]+1,ans);
				}
			}
		}
		else {
			for(int i = 1; i <= n; i++){
				ans = max(dp[i],ans);
			}
		}
		
		printf("%d\n", ans);
	}
	return 0;
}
```