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.util.*; 
import java.io.*;




public class B2 {
/*

 */
    public static BR in;
    public static LR lin;
    public static PrintWriter out;
    public static PrintWriter fout;
    static {
        try {
            in = new BR();
            out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out  ) ) );
            fout = new PrintWriter(new BufferedWriter(new OutputStreamWriter(new FileOutputStream("output.txt") ) ) );
        }
        catch (Exception e){
            
        }
    }
    
    public static boolean bg = true;
    public static void main(String[] args) throws Exception {
        s1();
        out.close();
    }
    
    static int n1 = 0;
    static int k1 = 0;
    static int[] l1 = null;
    static IntL[] al = null;
    static int[] max = null;
    static boolean[] ex = null;
    private static void s1() throws Exception {
        n1 = in.ni();
        k1 = in.ni();
        l1 = in.nil(n1);
        if (n1 <= 1){
            pn(0);
            return;
        }
        al = new IntL[n1];
        for (int i =0; i <al.length; i++){
            al[i] = new IntL();
        }
        max = new int[n1];
        ex = new boolean[n1];
        int low = 0;
        int high = 2000000000+10;
        for (;high - low>1;){
            long f1 = low;
            f1 += high;
            f1 /=2;
            int mid = (int)f1;
            int needed = n1 - check2(mid);
            if (needed > k1){
                low = mid;
            }
            else {
                high = mid;
            }
        }
        int need2 = n1 - check2(low);
        if (need2 > k1){
            pn(high);
        }
        else {
            pn(low);
        }
    }
    
    public static int check2(int lim){
        for (int i =0; i <al.length; i++){
            al[i].size = 0;
        }
        for (int i = 0; i < l1.length; i++){
            for (int j =i + 1;j<l1.length; j++){
                int diff = l1[j]-l1[i];
                if (diff < 0) diff *= -1;
                long upper = (long)(j-i)*(long)lim;
                if (diff <= upper){
                    al[i].add(j);
                }
            }
        }
        Arrays.fill(max, 1);
        Arrays.fill(ex, false);
        for (int i = 0 ; i < n1; i++){
            if (ex[i]){
                continue;
            }
            rec(i);
        }
        return max(max);
    }
    public static int rec(int n1){
        if (ex[n1]) return max[n1];
        for (int e: al[n1]){
            max[n1] = Math.max(max[n1], rec(e)+1);
        }
        ex[n1]=true;
        return max[n1];
    }
    
    private static void pn(Object... o1) {
        for (int i = 0; i < o1.length; i++) {
            if (i != 0) out.print(" ");
            out.print(o1[i]);
        }
        out.println();
    }

    private static int max(int ... l1){
        int fin = Integer.MIN_VALUE;
        for (int e: l1){
            if (e > fin) fin = e;
        }
        return fin;
    }
    
    private static class LR {
    }

    private static class BR {
        BufferedReader k1 = null;
        StringTokenizer k2 = null;

        public BR() {
            k1 = new BufferedReader(new InputStreamReader(System.in));
        }

        public String nx() throws Exception {
            for (;;) {
                if (k2 == null || !k2.hasMoreTokens()) {
                    String temp = k1.readLine();
                    if (temp == null) return null;
                    k2 = new StringTokenizer(temp);
                }
                else
                    break;
            }

            return k2.nextToken();
        }

        public int ni() throws Exception {
            return Integer.parseInt(nx());
        }

        public int[] nil(int n1) throws Exception {
            int[] fin = new int[n1];
            for (int i = 0; i < n1; i++) {
                fin[i] = Integer.parseInt(nx());
            }
            return fin;
        }
    }

    private static class IntL implements Iterable<Integer> {
        public int[] l1 = null;
        public int size = 0;

        public IntL(int initialCapacity) {
            this.l1 = new int[initialCapacity];
        }

        public IntL() {
            this(5);
        }

        public void add(int e) {
            if (size == l1.length) {
                l1 = Arrays.copyOf(l1, ((l1.length * 3) >> 1) + 1);
            }
            l1[size++] = e;
        }

        @Override
        public String toString() {
            StringBuilder fin = new StringBuilder();
            fin.append('{');
            for (int i = 0; i < size; i++) {
                if (i != 0) fin.append(", ");
                fin.append(l1[i]);
            }
            fin.append('}');
            return fin.toString();
        }
        
        @Override
        public Iterator<Integer> iterator() {
            return new It();
        }

        public class It implements Iterator<Integer> {
            int ptr = 0;

            @Override
            public boolean hasNext() {
                if (ptr < size) return true;
                return false;
            }

            @Override
            public Integer next() {
                int fin = l1[ptr];
                ptr++;
                return fin;
            }

            @Override
            public void remove() {

            }
        }
    }
    
}
