#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define vvi vector< vector<int> >
#define vi vector<int>
#define All(X) X.begin(),X.end()
#define FOR(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define pb push_back
#define pii pair<int,int>
#define mp make_pair
#define pi 3.14159265359
#define shosu(X) fixed << setprecision(X)
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}

int main(){
	while(1){
		int n,k;
		bool d[100001] = {false};
		int kyoyou = 0;
		cin >> n >> k;
		if(n == 0 && k == 0) break;
		REP(i,k){
			int t;
			cin >> t;
			if(t == 0){
				kyoyou = 1;
			}else{
				d[t] = true;
			}
		}
		int b,f;
		b = 1; f = 1;
		int space = 0;
		if(!d[b]) space++;
		int ans = 1;
		while ( b < n ){
			while (f <= n && space <= kyoyou){
				space += d[ ++f ] == false;
			}
			ans = max(ans, f-b);
			space -= d[ b++ ] == false;
		}
		cout << ans << endl;

	}	
}
### Prompt

Create a solution in CPP for 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 <bits/stdc++.h>
using namespace std;

#define ll long long
#define vvi vector< vector<int> >
#define vi vector<int>
#define All(X) X.begin(),X.end()
#define FOR(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define pb push_back
#define pii pair<int,int>
#define mp make_pair
#define pi 3.14159265359
#define shosu(X) fixed << setprecision(X)
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}

int main(){
	while(1){
		int n,k;
		bool d[100001] = {false};
		int kyoyou = 0;
		cin >> n >> k;
		if(n == 0 && k == 0) break;
		REP(i,k){
			int t;
			cin >> t;
			if(t == 0){
				kyoyou = 1;
			}else{
				d[t] = true;
			}
		}
		int b,f;
		b = 1; f = 1;
		int space = 0;
		if(!d[b]) space++;
		int ans = 1;
		while ( b < n ){
			while (f <= n && space <= kyoyou){
				space += d[ ++f ] == false;
			}
			ans = max(ans, f-b);
			space -= d[ b++ ] == false;
		}
		cout << ans << endl;

	}	
}
```