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
#include <iostream>
#include <cstring>
using namespace std;

int main(void){
	int data[100001];
	int ans=0;
	int a;
	int n,k;
	while(1){
		cin >> n >> k;
		if(n==0 && k==0)break;
		ans=0;
		memset(data,0,sizeof(data));
		for(a=0;a<k;a++){
			int b;
			cin >> b;
			data[b]=1;
		}
		if(data[0]==0){
			int res=0;
			for(a=1;a<=n;a++){
				if(data[a]==1){
					res++;
					ans=max(ans,res);
				}else{
					res=0;
				}
			}
		}else{
			int res=0,x1=0,x2=0;
			bool zero=false;
			for(a=1;a<=n;a++){
				if(data[a]==1){
					res++;
					x1++;
					ans=max(ans,res);
				}else{
					if(zero){
						res=res-x2;
						x2=x1;
						x1=0;
					}else{
						res++;
						x2=x1;
						x1=0;
						zero=true;
					}
				}
			}
		}
		cout << ans << endl;
	}
	return 0;
}