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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "khokharnikunj8", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            DLevkoAndArray solver = new DLevkoAndArray();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DLevkoAndArray {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int k = in.readInt();
            long[] ar = new long[n];
            for (int i = 0; i < n; i++) ar[i] = in.readInt();
            long low = 0;
            long high = 10000000000l;
            long index = Long.MIN_VALUE;
            while (low <= high) {
                long mid = (low + high) >> 1;
                int[] dp = new int[n + 2];
                for (int i = 0; i <= n + 1; i++) dp[i] = i - 1;
                for (int i = 1; i <= n + 1; i++) {
                    for (int j = i + 1; j <= n + 1; j++) {
                        if (j == n + 1 || (Math.abs(ar[j - 1] - ar[i - 1]) <= mid * ((long) (j - i))))
                            dp[j] = Math.min(dp[j], dp[i] + (j - i - 1));
                    }
                }
                int ans = Integer.MAX_VALUE;
                for (int i = 1; i <= n; i++) {
                    ans = Math.min(ans, dp[i] + (n - i));
                }
                if (ans <= k) {
                    index = mid;
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }
            out.println(index);
        }

    }

    static class FastInput {
        private final InputStream is;
        private final byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private final Writer os;
        private final StringBuilder cache = new StringBuilder(5 << 20);

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(long c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }
}

