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.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.util.Arrays;

public class B360 {
	
	final int oo = 987654321;
	
	int n, k;
	int[] a;
	
	long diff;
	int[][] memo;
	
	int getDifference(int cur, int prev) {
		if(prev == -1) return 0;
		return Math.abs(a[cur] - a[prev]);
	}
	
	int dp(int prev, int cur) {
		if(cur == n) return 0;
		if(memo[prev + 1][cur] != -1) return memo[prev + 1][cur];
		int change = 1 + dp(prev, cur + 1);
		int stay = oo;
		{
			long changed = cur - prev;
			long fluctuate = changed * diff;
			int cdiff = getDifference(cur, prev);
//			System.out.printf("prev: %d cur: %d, changed is %d, fluctuation allowed is %d, and current difference is %d\n", prev, cur, changed, fluctuate, cdiff);
			if(cdiff <= fluctuate) stay = dp(cur, cur + 1);
		}
		int ans = Math.min(change, stay);
		memo[prev + 1][cur] = ans;
		return ans;
	}
	
	boolean check(long mid) {
		diff = mid;
		for(int[] a : memo) Arrays.fill(a, -1);
		long minCut = dp(-1, 0);
//		System.out.println("mincut = " + minCut);
		return minCut <= k;
	}
	
	public void solve(JS in, PrintWriter out) {
		n = in.nextInt();
		k = in.nextInt();
		a = new int[n];
		memo = new int[n + 1][n];
		for(int i = 0; i < n; ++i) a[i] = in.nextInt();
//		System.out.println(check(1000));
		boolean debug = !true;
		if(debug) return;
		long lo = 0, hi = (int) 2e9;
		while(lo <= hi) {
//			System.out.println(lo + " " + hi);
			long mid = lo + hi >> 1;
			if(check(mid)) hi = mid - 1;
			else lo = mid + 1;
		}
		out.println(lo);
	}
	
	public static void main(String[] args) {
		JS in = new JS();
		PrintWriter out = new PrintWriter(System.out);
		new B360().solve(in, out);
		out.close();
	}
	
	static class JS {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}

		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
}
