#include <bits/stdc++.h>
using namespace std;
const int inf = 0x3fffffff;
const int maxn = 1000005;
int u[maxn], w[maxn], a[5005], k, n;
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d", &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 ans = 1; ans <= a[n] + 1; ans++) {
    int cnt = 0;
    for (int j = ans; j <= a[n]; j += ans) cnt += w[j];
    if (cnt > k * (k + 1) / 2) continue;
    cnt = 0;
    for (int j = 1; j <= n; j++) {
      int x = a[j] % ans;
      if (u[x] == ans) cnt++;
      u[x] = ans;
    }
    if (cnt <= k) {
      printf("%d\n", ans);
      break;
    }
  }
  return 0;
}

### Prompt

Please formulate a Cpp solution to 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;
const int inf = 0x3fffffff;
const int maxn = 1000005;
int u[maxn], w[maxn], a[5005], k, n;
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d", &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 ans = 1; ans <= a[n] + 1; ans++) {
    int cnt = 0;
    for (int j = ans; j <= a[n]; j += ans) cnt += w[j];
    if (cnt > k * (k + 1) / 2) continue;
    cnt = 0;
    for (int j = 1; j <= n; j++) {
      int x = a[j] % ans;
      if (u[x] == ans) cnt++;
      u[x] = ans;
    }
    if (cnt <= k) {
      printf("%d\n", ans);
      break;
    }
  }
  return 0;
}

```