#include<stdio.h>
#include<algorithm>
using namespace std;
int now[100000];
int failure[100000];
bool ok[100000];
int main(){
	int a,b;
	while(scanf("%d%d",&a,&b),a){
		for(int i=0;i<a;i++)ok[i]=false;
		bool zero=false;
		for(int i=0;i<b;i++){
			int c;
			scanf("%d",&c);
			if(c==0)zero=true;
			else ok[c-1]=true;
		}
		now[0]=1;
		if(ok[0])failure[0]=1;
		else failure[0]=0;
		for(int i=1;i<a;i++){
			if(ok[i]){
				failure[i]=failure[i-1]+1;
				now[i]=now[i-1]+1;
			}else{
				failure[i]=0;
				now[i]=failure[i-1]+1;
			}
		}
		int ret=0;
		for(int i=0;i<a;i++)ret=max(ret,zero?now[i]:failure[i]);
		printf("%d\n",ret);
	}
}
### 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<stdio.h>
#include<algorithm>
using namespace std;
int now[100000];
int failure[100000];
bool ok[100000];
int main(){
	int a,b;
	while(scanf("%d%d",&a,&b),a){
		for(int i=0;i<a;i++)ok[i]=false;
		bool zero=false;
		for(int i=0;i<b;i++){
			int c;
			scanf("%d",&c);
			if(c==0)zero=true;
			else ok[c-1]=true;
		}
		now[0]=1;
		if(ok[0])failure[0]=1;
		else failure[0]=0;
		for(int i=1;i<a;i++){
			if(ok[i]){
				failure[i]=failure[i-1]+1;
				now[i]=now[i-1]+1;
			}else{
				failure[i]=0;
				now[i]=failure[i-1]+1;
			}
		}
		int ret=0;
		for(int i=0;i<a;i++)ret=max(ret,zero?now[i]:failure[i]);
		printf("%d\n",ret);
	}
}
```