#include <iostream>
#include <algorithm>
#include <cstring>

constexpr int MAX_N=100000;

int n,k;
int dp[MAX_N+1][2];//???????????????????????????????????°???????????????????´?????????????????????£???????????????
bool IsNum[MAX_N+1];
bool IsWhiteCard;

int main(){
	while(std::cin>>n>>k){
		if(n+k==0)
			break;
		std::memset(dp,0,sizeof(dp));
		std::memset(IsNum,0,sizeof(IsNum));
		int a;
		for(int i=0;i<k;++i){
			std::cin>>a;
			if(a==0)
				IsWhiteCard=true;
			else
				IsNum[a]=true;
		}

		for(int i=1;i<=n;++i) {
			if(IsNum[i]){
				dp[i][0]=dp[i-1][0]+1;
				dp[i][1]=dp[i-1][1]+1;
			}
		else if(IsWhiteCard)
			dp[i][1]=dp[i-1][0]+1;
		}
		int ans=0;
		for(int i=1;i<=n;++i){
			ans=std::max(ans,dp[i][1]);
		}
		std::cout<<ans<<std::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 <iostream>
#include <algorithm>
#include <cstring>

constexpr int MAX_N=100000;

int n,k;
int dp[MAX_N+1][2];//???????????????????????????????????°???????????????????´?????????????????????£???????????????
bool IsNum[MAX_N+1];
bool IsWhiteCard;

int main(){
	while(std::cin>>n>>k){
		if(n+k==0)
			break;
		std::memset(dp,0,sizeof(dp));
		std::memset(IsNum,0,sizeof(IsNum));
		int a;
		for(int i=0;i<k;++i){
			std::cin>>a;
			if(a==0)
				IsWhiteCard=true;
			else
				IsNum[a]=true;
		}

		for(int i=1;i<=n;++i) {
			if(IsNum[i]){
				dp[i][0]=dp[i-1][0]+1;
				dp[i][1]=dp[i-1][1]+1;
			}
		else if(IsWhiteCard)
			dp[i][1]=dp[i-1][0]+1;
		}
		int ans=0;
		for(int i=1;i<=n;++i){
			ans=std::max(ans,dp[i][1]);
		}
		std::cout<<ans<<std::endl;
	}
	return 0;
}
```