#include <iostream>
#include <vector>
#include <string>
#include <queue>
#include <algorithm>
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,b) FOR(i,0,b)
using namespace std;
typedef long long ll;
const int INF=1<<30;
typedef vector<int> vi;
int DP[100001][2];
bool card[100001];
int main() {
	int n,k;
	while(cin >> n >> k && n){
	REP(i,100001)
		card[i]=false;
	REP(i,100001)
		REP(j,2)
			DP[i][j]=false;
	int tmp,maxim=0;
	REP(i,k){
	cin >> tmp;
	card[tmp]=true;
	}
	maxim=0;
	if(card[1]){
	DP[1][0]=1;
	maxim=1;
	}
	if(card[1]||card[0])
	DP[1][1]=1;
	FOR(i,2,n+1){
		if(card[i]){
		DP[i][0]=DP[i-1][0]+1;
		DP[i][1]=DP[i-1][1]+1;
		}
		else{
		DP[i][0]=0;
		DP[i][1]=DP[i-1][0]+1;
		}
		maxim=max(maxim,DP[i][0]);
		if(card[0])
		maxim=max(maxim,DP[i][1]);
	}
	cout << maxim << endl;
	}
	// your code goes here
	return 0;
}
### Prompt

Please create a solution in cpp 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 <vector>
#include <string>
#include <queue>
#include <algorithm>
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,b) FOR(i,0,b)
using namespace std;
typedef long long ll;
const int INF=1<<30;
typedef vector<int> vi;
int DP[100001][2];
bool card[100001];
int main() {
	int n,k;
	while(cin >> n >> k && n){
	REP(i,100001)
		card[i]=false;
	REP(i,100001)
		REP(j,2)
			DP[i][j]=false;
	int tmp,maxim=0;
	REP(i,k){
	cin >> tmp;
	card[tmp]=true;
	}
	maxim=0;
	if(card[1]){
	DP[1][0]=1;
	maxim=1;
	}
	if(card[1]||card[0])
	DP[1][1]=1;
	FOR(i,2,n+1){
		if(card[i]){
		DP[i][0]=DP[i-1][0]+1;
		DP[i][1]=DP[i-1][1]+1;
		}
		else{
		DP[i][0]=0;
		DP[i][1]=DP[i-1][0]+1;
		}
		maxim=max(maxim,DP[i][0]);
		if(card[0])
		maxim=max(maxim,DP[i][1]);
	}
	cout << maxim << endl;
	}
	// your code goes here
	return 0;
}
```