Levko has an array that consists of integers: a1, a2, ... , an. But he doesn’t like this array at all.

Levko thinks that the beauty of the array a directly depends on value c(a), which can be calculated by the formula: 

<image> The less value c(a) is, the more beautiful the array is.

It’s time to change the world and Levko is going to change his array for the better. To be exact, Levko wants to change the values of at most k array elements (it is allowed to replace the values by any integers). Of course, the changes should make the array as beautiful as possible.

Help Levko and calculate what minimum number c(a) he can reach.

Input

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 2000). The second line contains space-separated integers a1, a2, ... , an ( - 109 ≤ ai ≤ 109).

Output

A single number — the minimum value of c(a) Levko can get.

Examples

Input

5 2
4 7 4 7 4


Output

0


Input

3 1
-100 0 100


Output

100


Input

6 3
1 2 3 7 8 9


Output

1

Note

In the first sample Levko can change the second and fourth elements and get array: 4, 4, 4, 4, 4.

In the third sample he can get array: 1, 2, 3, 4, 5, 6.
#include <bits/stdc++.h>
using namespace std;
int MODP(long long x) {
  int r = x % 1000000007;
  if (r < 0) r += 1000000007;
  return r;
}
template <class T>
class BinaryIndexedTree {
  vector<T> val;
  int n, minIndex, maxIndex;

 public:
  BinaryIndexedTree(int n) : BinaryIndexedTree(1, n) {}
  BinaryIndexedTree(int minIndex, int maxIndex) { init(minIndex, maxIndex); }
  BinaryIndexedTree() {}
  void init(int minIndex, int maxIndex) {
    this->minIndex = minIndex;
    this->maxIndex = maxIndex;
    this->n = maxIndex - minIndex + 1;
    val.resize(n + 1);
  }
  void add(int i, int v) {
    i = i - minIndex + 1;
    for (; i <= n; i += i & -i) {
      val[i] += v;
    }
  }
  T sum(int i) {
    i = i - minIndex + 1;
    if (i <= 0) return 0;
    if (i > n) i = n;
    T s = 0;
    for (; i > 0; i -= i & -i) s += val[i];
    return s;
  }
  T sum(int i1, int i2) { return sum(i2) - sum(i1 - 1); }
};
template <class T>
class RangeUpdateArray {
  BinaryIndexedTree<T> tree;
  int minIndex, maxIndex;

 public:
  RangeUpdateArray(int n) : RangeUpdateArray(1, n) {}
  RangeUpdateArray(int minIndex, int maxIndex) {
    this->minIndex = minIndex;
    this->maxIndex = maxIndex;
    tree.init(minIndex, maxIndex);
  }
  void add(int i, int j, T v) {
    assert(minIndex <= i && i <= j && j <= maxIndex);
    if (j < maxIndex) {
      tree.add(j + 1, -v);
    }
    tree.add(i, v);
  }
  T get(int i) {
    assert(minIndex <= i && i <= maxIndex);
    return tree.sum(i);
  }
  const T operator[](int i) { return get(i); }
};
class BinarySearch {
 public:
  template <class T>
  static T binarySearchMin(const T &minIndex, const T &maxIndex,
                           const function<bool(T)> &predicate) {
    T leftIndex = minIndex, rightIndex = maxIndex, midIndex, ret = maxIndex + 1;
    while (leftIndex <= rightIndex) {
      midIndex = leftIndex + (rightIndex - leftIndex) / 2;
      if (predicate(midIndex)) {
        ret = midIndex;
        rightIndex = midIndex - 1;
      } else {
        leftIndex = midIndex + 1;
      }
    }
    return ret;
  }
  template <class T>
  static T binarySearchMax(const T &minIndex, const T &maxIndex,
                           const function<bool(T)> &predicate) {
    T leftIndex = minIndex, rightIndex = maxIndex, midIndex, ret = minIndex - 1;
    while (leftIndex <= rightIndex) {
      midIndex = leftIndex + (rightIndex - leftIndex) / 2;
      if (predicate(midIndex)) {
        ret = midIndex;
        leftIndex = midIndex + 1;
      } else {
        rightIndex = midIndex - 1;
      }
    }
    return ret;
  }
  static double binarySearchMaxReal(double minRange, double maxRange,
                                    double epsilon,
                                    const function<bool(double)> &predicate) {
    double l = minRange, r = maxRange, m, ret = maxRange + 1;
    while (r - l > epsilon) {
      m = l + (r - l) / 2;
      if (predicate(m)) {
        ret = m;
        l = m;
      } else {
        r = m;
      }
    }
    return ret;
  }
  static double binarySearchMinReal(double minRange, double maxRange,
                                    double epsilon,
                                    const function<bool(double)> &predicate) {
    double l = minRange, r = maxRange, m, ret = maxRange + 1;
    while (r - l > epsilon) {
      m = l + (r - l) / 2;
      if (predicate(m)) {
        l = m;
        ret = m;
      } else {
        r = m;
      }
    }
    return ret;
  }
};
void testGen() {
  freopen("biginput1.txt", "w", stdout);
  fclose(stdout);
}
int val(const vector<int> &a, int l, int r) {
  int len = r - l;
  int diff = abs(a[r] - a[l]);
  int ans = diff / len;
  if (diff % len != 0) {
    ans++;
  }
  return ans;
}
bool ok(const vector<int> &a, int k, int target) {
  int n = (int)a.size() - 1;
  vector<int> f(n + 1);
  for (auto i = 1; i <= n; ++i) {
    f[i] = 1;
    for (auto j = 1; j <= i - 1; ++j) {
      if (val(a, j, i) <= target) {
        f[i] = max(f[i], f[j] + 1);
      }
    }
  }
  int t = 0;
  for (auto i = 1; i <= n; ++i) {
    t = max(t, f[i]);
  }
  if (n - t <= k) {
    return true;
  }
  return false;
}
int main() {
  ios::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  vector<int> a(n + 1);
  for (auto i = 1; i <= n; ++i) cin >> a[i];
  int cur = 0;
  for (auto i = 2; i <= n; ++i) {
    cur = max(cur, abs(a[i] - a[i - 1]));
  }
  int ans = BinarySearch::binarySearchMin<int>(
      0, cur, [&](int target) { return ok(a, k, target); });
  cout << ans << endl;
  return 0;
}
