#include <bits/stdc++.h>
using namespace std;
int n, k;
int a[5010];
int w[1000010], u[1000010];
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  sort(a + 1, a + n + 1);
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j < i; ++j) ++w[a[i] - a[j]];
  for (int i = 1; i <= a[n] + 1; ++i) {
    int t = 0;
    for (int j = i; j <= a[n]; j += i) t += w[j];
    if (t > k * (k + 1) / 2) continue;
    t = 0;
    for (int j = 1; j <= n; ++j) {
      int x = a[j] % i;
      if (u[x] == i) ++t;
      u[x] = i;
    }
    if (t <= k) {
      cout << i << endl;
      return 0;
    }
  }
  puts("-1");
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

You have been given n distinct integers a1, a2, ..., an. You can remove at most k of them. Find the minimum modular m (m > 0), so that for every pair of the remaining integers (ai, aj), the following unequality holds: <image>.

Input

The first line contains two integers n and k (1 ≤ n ≤ 5000, 0 ≤ k ≤ 4), which we have mentioned above. 

The second line contains n distinct integers a1, a2, ..., an (0 ≤ ai ≤ 106).

Output

Print a single positive integer — the minimum m.

Examples

Input

7 0
0 2 3 6 7 12 18


Output

13


Input

7 1
0 2 3 6 7 12 18


Output

7

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n, k;
int a[5010];
int w[1000010], u[1000010];
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  sort(a + 1, a + n + 1);
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j < i; ++j) ++w[a[i] - a[j]];
  for (int i = 1; i <= a[n] + 1; ++i) {
    int t = 0;
    for (int j = i; j <= a[n]; j += i) t += w[j];
    if (t > k * (k + 1) / 2) continue;
    t = 0;
    for (int j = 1; j <= n; ++j) {
      int x = a[j] % i;
      if (u[x] == i) ++t;
      u[x] = i;
    }
    if (t <= k) {
      cout << i << endl;
      return 0;
    }
  }
  puts("-1");
  return 0;
}

```