#include "bits/stdc++.h"

using namespace std;

const char en = '\n';
using  ll =          long long;
using ull = unsigned long long;


using Bitset = bitset<100001>;
int n,k;

int main(){
	ios::sync_with_stdio(false);cin.tie();
	while(true){
		cin>>n>>k;
		if(n==0&&k==0) break;

		Bitset b;
		int buf;
		for(int i=0;i<k;i++){
			cin>>buf;
			b.set(buf);
		}
		deque<int> d;
		for(int i=1;i<=n;i++){
			if(!b[i])
				d.push_back(i);
		}
		d.push_front(0);
		d.push_back (n+1);


		int result=0;
		if(b[0]){

			int befA=d.front();	d.pop_front();
			int befB=d.front();	d.pop_front();
			while(!d.empty()){
				buf =d.front();	d.pop_front();
				result=max(result,buf-befA-1);
				befA=befB;
				befB=buf;
			}
			cout<<result<<en;

		}else{

			int before=d.front();	d.pop_front();
			while(!d.empty()){
				buf=d.front();	d.pop_front();
				result=max(result,buf-before-1);
				before=buf;
			}
			cout<<result<<en;

		}
		/*
		while(!d.empty()){
			cout<<d.front()<<en;
			d.pop_front();
		}
		cout<<en;
		*/
	}
	return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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;

const char en = '\n';
using  ll =          long long;
using ull = unsigned long long;


using Bitset = bitset<100001>;
int n,k;

int main(){
	ios::sync_with_stdio(false);cin.tie();
	while(true){
		cin>>n>>k;
		if(n==0&&k==0) break;

		Bitset b;
		int buf;
		for(int i=0;i<k;i++){
			cin>>buf;
			b.set(buf);
		}
		deque<int> d;
		for(int i=1;i<=n;i++){
			if(!b[i])
				d.push_back(i);
		}
		d.push_front(0);
		d.push_back (n+1);


		int result=0;
		if(b[0]){

			int befA=d.front();	d.pop_front();
			int befB=d.front();	d.pop_front();
			while(!d.empty()){
				buf =d.front();	d.pop_front();
				result=max(result,buf-befA-1);
				befA=befB;
				befB=buf;
			}
			cout<<result<<en;

		}else{

			int before=d.front();	d.pop_front();
			while(!d.empty()){
				buf=d.front();	d.pop_front();
				result=max(result,buf-before-1);
				before=buf;
			}
			cout<<result<<en;

		}
		/*
		while(!d.empty()){
			cout<<d.front()<<en;
			d.pop_front();
		}
		cout<<en;
		*/
	}
	return 0;
}
```