#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>

#define MAX_N 100000

using namespace std;

int field[MAX_N];
int dp[MAX_N + 1][2];

int n;
int k;

bool flag = false;

int ans;

void solve(){
	for(int i = 0;i < MAX_N;i++){
		dp[i][0] = 1;
		dp[i][1] = 2;
	}

	sort(field,field + k);

	for(int i = 0;i < k;i++){
		if(field[i + 1] == field[i] + 1){
			dp[i + 1][0] = max(dp[i + 1][0],dp[i][0] + 1);
			dp[i + 1][1] = max(dp[i + 1][1],dp[i][1] + 1);
		}
		else if(field[i + 1] == field[i] + 2){
			dp[i + 1][1] = max(dp[i + 1][1],dp[i][0] + 2);
		}
	}

	ans = 0;
	for(int i = 0;i < k;i++){
		ans = max(ans,dp[i][0]);
	}
	if(flag){
		for(int i = 0;i < k;i++){
			ans = max(ans,dp[i][1]);
		}
	}

	return ;
}

int main (){

	while(true){

	scanf("%d%d",&n,&k);
	if(n == 0 && k == 0)break;
	flag = false;
	for(int i = 0;i < k;i++){
		scanf("%d",field + i);
		if(field[i] == 0) flag = true;
	}

	solve();

	printf("%d\n",ans);
		
	}

	return 0;
}
### Prompt

Your challenge is to write 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 <cstdio>
#include <cmath>
#include <algorithm>

#define MAX_N 100000

using namespace std;

int field[MAX_N];
int dp[MAX_N + 1][2];

int n;
int k;

bool flag = false;

int ans;

void solve(){
	for(int i = 0;i < MAX_N;i++){
		dp[i][0] = 1;
		dp[i][1] = 2;
	}

	sort(field,field + k);

	for(int i = 0;i < k;i++){
		if(field[i + 1] == field[i] + 1){
			dp[i + 1][0] = max(dp[i + 1][0],dp[i][0] + 1);
			dp[i + 1][1] = max(dp[i + 1][1],dp[i][1] + 1);
		}
		else if(field[i + 1] == field[i] + 2){
			dp[i + 1][1] = max(dp[i + 1][1],dp[i][0] + 2);
		}
	}

	ans = 0;
	for(int i = 0;i < k;i++){
		ans = max(ans,dp[i][0]);
	}
	if(flag){
		for(int i = 0;i < k;i++){
			ans = max(ans,dp[i][1]);
		}
	}

	return ;
}

int main (){

	while(true){

	scanf("%d%d",&n,&k);
	if(n == 0 && k == 0)break;
	flag = false;
	for(int i = 0;i < k;i++){
		scanf("%d",field + i);
		if(field[i] == 0) flag = true;
	}

	solve();

	printf("%d\n",ans);
		
	}

	return 0;
}
```