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>
using namespace std;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int n,k,num;
  while(cin >> n >> k) {
    if(n+k == 0) break;
    vector<int> seq(n+1,-1);
    for(int i=1;i<=k;i++) {
      cin >> num;
      seq[num] = num;
    }
    int max_cnt,cnt;
    max_cnt = cnt = 0;
    if(seq[0] == -1) {
      for(int i=1;i<=n;i++) {
        if(seq[i] == -1) {
          max_cnt = max(max_cnt,cnt);
          cnt = 0;
        }
        else {
          cnt++;
        }
      }
    }
    else {
      bool use_empty = false;
      int bf_i;
      for(int i=1;i<=n;i++) {
        if(seq[i] == -1) {
          max_cnt = max(max_cnt,cnt);
          if(!use_empty) {
            use_empty = true;
            bf_i = i;
            cnt++;
          }
          else {
            use_empty = false;
            i = bf_i;
            cnt = 0;
          }
        }
        else {
          cnt++;
        }
      }
    }
    max_cnt = max(max_cnt,cnt);
    cout << max_cnt << endl;
  }
}