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 <vector>
#include <algorithm>
#include <queue>
using namespace std;

int main() {
  int n,k,ck=0;
  while(cin >> n >> k && (n!=0 || k!=0)) {
    vector<int> a(n+1);
    for(int i=0; i<n+1; i++) a[i]=0;
    while(k--) {
      int x;
      cin >> x;
      if(x!=0) a[x]=1;
      if(x==0) ck=1;
    }
    int max=0,cnt=0;
    if(ck==0) {
      for(int i=1; i<=n; i++) {
	if(a[i]) {
	  cnt++;
	  if(cnt>max) max=cnt;
	} else {
	  cnt=0;
	}
      }
    } else {
      queue<int>que;
      for(int i=1; i<=n; i++) {
	if(a[i-1]==0) que.push(i);
      }
      while(!que.empty()) {
	int z=que.front(), k=1;
	que.pop();
	cnt=0;
	int i;
	for(i=z; i<=n; i++) {
	  if(a[i]==0) k--;
	  if(k<0) break;
	  cnt++;
	  if(cnt>max) max=cnt;
	}
      }
    }  
    
    cout << max << endl;
  }
  return 0;
}
