#include <bits/stdc++.h>
//#define int long long

using namespace std;
using LL = long long;
using P = pair<int, int>;

#define FOR(i, a, n) for(int i = (int)(a); i < (int)(n); ++i)
#define REP(i, n) FOR(i, 0, n)

#define pb(a) push_back(a)
#define all(x) (x).begin(),(x).end()

const int INF = (int)1e9;
const LL INFL = (LL)1e19;
const int MOD = 1e9 + 7;

signed main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int n, k;
    while(cin >> n >> k, n + k > 0)
    {
        vector<bool> a(n+1, 0);
        REP(i, k)
        {
            int x; cin >> x;
            a[x] = true;
        }

        int ans = 0;
        int cnt = 0;
        vector<vector<int>> dp(n+1, vector<int>(2, 0));

        REP(i, n)
        {
            if(a[i+1]) dp[i+1][0] = dp[i][0] + 1, dp[i+1][1] = dp[i][1] + 1;
            else dp[i+1][0] = 0, dp[i+1][1] = dp[i][0] + 1;

            ans = max({ans, dp[i+1][0], a[0] ? dp[i+1][1] : 0});
        }
        cout << ans << endl;
    }
}

### Prompt

Your challenge is to write a CPP solution 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 <bits/stdc++.h>
//#define int long long

using namespace std;
using LL = long long;
using P = pair<int, int>;

#define FOR(i, a, n) for(int i = (int)(a); i < (int)(n); ++i)
#define REP(i, n) FOR(i, 0, n)

#define pb(a) push_back(a)
#define all(x) (x).begin(),(x).end()

const int INF = (int)1e9;
const LL INFL = (LL)1e19;
const int MOD = 1e9 + 7;

signed main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int n, k;
    while(cin >> n >> k, n + k > 0)
    {
        vector<bool> a(n+1, 0);
        REP(i, k)
        {
            int x; cin >> x;
            a[x] = true;
        }

        int ans = 0;
        int cnt = 0;
        vector<vector<int>> dp(n+1, vector<int>(2, 0));

        REP(i, n)
        {
            if(a[i+1]) dp[i+1][0] = dp[i][0] + 1, dp[i+1][1] = dp[i][1] + 1;
            else dp[i+1][0] = 0, dp[i+1][1] = dp[i][0] + 1;

            ans = max({ans, dp[i+1][0], a[0] ? dp[i+1][1] : 0});
        }
        cout << ans << endl;
    }
}

```