#include <bits/stdc++.h>
using namespace std;
#define Rep(i,N) for(int i = 0; i < N; i++)
#define INF 1 << 28

inline void chmax(int &a, int b) { a = max(a,b); }
inline void chmin(int &a, int b) { a = min(a,b); }

int main()
{
  int N, K;
  while(cin >> N >> K, N || K) {
    int large[100007] = {0};
    bool flag = false;
    int A;
    Rep(i,K) {
      cin >> A;
      if(A)large[A]++;
      else flag = true;
    }
    Rep(i,N + 1) {
      if(large[i + 1] > 0)large[i + 1] = large[i] + 1;
    }
    int val = large[N - 1];
    for(int i = N + 1; i >= 1; i--) {
      if(large[i] > 0) {
	large[i] = val;
      } else {
	val = large[i - 1];
      }
    }
    int maxv = -INF;
    for(int i = 1; i <= N + 1; i++) {
      if(large[i]) {
	chmax(maxv,large[i]);
      } else if(flag) {
	chmax(maxv,1 + large[i - 1] + large[i + 1]);
      } else {
	chmax(maxv,0);
      }
    }
    cout << maxv << endl;
  }
  return 0;
}
### 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 Rep(i,N) for(int i = 0; i < N; i++)
#define INF 1 << 28

inline void chmax(int &a, int b) { a = max(a,b); }
inline void chmin(int &a, int b) { a = min(a,b); }

int main()
{
  int N, K;
  while(cin >> N >> K, N || K) {
    int large[100007] = {0};
    bool flag = false;
    int A;
    Rep(i,K) {
      cin >> A;
      if(A)large[A]++;
      else flag = true;
    }
    Rep(i,N + 1) {
      if(large[i + 1] > 0)large[i + 1] = large[i] + 1;
    }
    int val = large[N - 1];
    for(int i = N + 1; i >= 1; i--) {
      if(large[i] > 0) {
	large[i] = val;
      } else {
	val = large[i - 1];
      }
    }
    int maxv = -INF;
    for(int i = 1; i <= N + 1; i++) {
      if(large[i]) {
	chmax(maxv,large[i]);
      } else if(flag) {
	chmax(maxv,1 + large[i - 1] + large[i + 1]);
      } else {
	chmax(maxv,0);
      }
    }
    cout << maxv << endl;
  }
  return 0;
}
```