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.
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.Reader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.List;
import java.util.StringTokenizer;

public class B2 {

    private static final long MODULO = (long) (1e9 + 7);
    private static final int INF = (int) (1e9 + 10);

    public static void main(String[] args) {
        BufferedScanner scanner = new BufferedScanner();
        PrintWriter writer = new PrintWriter(new BufferedOutputStream(System.out));

        int t = 1;//scanner.nextInt();
        for (int tc = 0; tc < t; tc++) {
            int n = scanner.nextInt();
            int k = scanner.nextInt();
//            int n = 2000;
//            int k = n / 2;
//            Random r = new Random(System.nanoTime());
            int[] a = new int[n];
            int min = INF;
            int max = -INF;
            for (int i = 0; i < n; i++) {
                a[i] = scanner.nextInt();
//                a[i] = r.nextInt((int) 1e9 + 1);
                min = Math.min(min, a[i]);
                max = Math.max(max, a[i]);
            }
            long time = System.nanoTime();
            if (n == 1) {
                writer.println(0);
                continue;
            }

            int[][] g = new int[n][n];
            int[][] gOrder = new int[n][];
            for (int i = 0; i < n; i++) {
                List<Integer> tmp = new ArrayList<>();
                for (int j = i + 1; j < n; j++) {
                    g[i][j] = g(i, j, a);
                    tmp.add(j);
                }
                int finalI = i;
                tmp.sort(Comparator.comparingInt(j -> g[finalI][j]));
                gOrder[i] = new int[tmp.size()];
                int j = 0;
                for (Integer item : tmp) {
                    gOrder[i][j++] = item;
                }
//                for (int j = 0; j < tmp.size(); j++) {
//                    gOrder[i][j] = tmp.get(j);
//                }
            }

            System.err.println("finish g: " + (System.nanoTime() - time) / 1e9);

            int low = 0, high = max - min;
            int ans = -1;
            while (low <= high) {
                int mid = low + (high - low) / 2;
                if (feasible(mid, a, n, k, g, gOrder)) {
                    ans = mid;
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }
            writer.println(ans);

            System.err.println("time: " + (System.nanoTime() - time) / 1e9);
        }

        scanner.close();
        writer.flush();
        writer.close();
    }

    private static int g(int i, int j, int[] a) {
        return (int) Math.ceil((double) Math.abs(a[i] - a[j]) / Math.abs(i - j));
    }

    static class Pair {
        final int first;
        final int second;

        Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }
    }

    private static boolean feasible(int cMax, int[] a, int n, int k, int[][] g, int[][] gOrder) {
        int[] f = new int[n];
        Arrays.fill(f, 1);
        for (int i = 0; i < n; i++) {
            if (f[i] >= n - k) {
                return true;
            }
            for (int j : gOrder[i]) {
                if (g[i][j] > cMax) {
                    break;
                }
                f[j] = Math.max(f[j], f[i] + 1);
            }
        }
        return false;
    }

    static class ListInt extends ArrayList<Integer> {}

    public static class BufferedScanner {
        BufferedReader br;
        StringTokenizer st;

        public BufferedScanner(Reader reader) {
            br = new BufferedReader(reader);
        }

        public BufferedScanner() {
            this(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

    }

    static long gcd(long a, long b) {
        if (a < b) {
            return gcd(b, a);
        }
        while (b > 0) {
            long tmp = b;
            b = a % b;
            a = tmp;
        }
        return a;
    }

    static long inverse(long a, long m) {
        long[] ans = extgcd(a, m);
        return ans[0] == 1 ? (ans[1] + m) % m : -1;
    }

    private static long[] extgcd(long a, long m) {
        if (m == 0) {
            return new long[]{a, 1, 0};
        } else {
            long[] ans = extgcd(m, a % m);
            long tmp = ans[1];
            ans[1] = ans[2];
            ans[2] = tmp;
            ans[2] -= ans[1] * (a / m);
            return ans;
        }
    }

    static long add(long a, long b) {
        a += b;
        if (a >= MODULO) {
            a -= MODULO;
        }
        return a;
    }

    static long sub(long a, long b) {
        a -= b;
        if (a < 0) {
            a += MODULO;
        }
        return a;
    }

    static long mul(long a, long b) {
        return a * b % MODULO;
    }

    static long div(long a, long b) {
        return a * inverse(b, MODULO) % MODULO;
    }

    static class Comb {
        final long modulo;
        final long[] fac, fnv;

        Comb(int limit, long modulo) {
            fac = new long[limit + 1];
            fnv = new long[limit + 1];
            fac[0] = 1;
            fnv[0] = 1;
            for (int i = 1; i <= limit; i++) {
                fac[i] = mul(fac[i - 1], i);
                fnv[i] = div(fnv[i - 1], i);
            }
            this.modulo = modulo;
        }

        long c(int total, int choose) {
            if (total < choose) {
                return 0;
            }
            if (total == 0 || total == choose) {
                return 1;
            }
            return mul(mul(fac[total], fnv[choose]), fnv[total - choose]);
        }
    }

}
