Problem: Roma found a new character in the game "World of Darkraft - 2". In this game the character fights monsters, finds the more and more advanced stuff that lets him fight stronger monsters.

The character can equip himself with k distinct types of items. Power of each item depends on its level (positive integer number). Initially the character has one 1-level item of each of the k types.

After the victory over the monster the character finds exactly one new randomly generated item. The generation process looks as follows. Firstly the type of the item is defined; each of the k types has the same probability. Then the level of the new item is defined. Let's assume that the level of player's item of the chosen type is equal to t at the moment. Level of the new item will be chosen uniformly among integers from segment [1; t + 1].

From the new item and the current player's item of the same type Roma chooses the best one (i.e. the one with greater level) and equips it (if both of them has the same level Roma choses any). The remaining item is sold for coins. Roma sells an item of level x of any type for x coins.

Help Roma determine the expected number of earned coins after the victory over n monsters.

Input

The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 100).

Output

Print a real number — expected number of earned coins after victory over n monsters. The answer is considered correct if its relative or absolute error doesn't exceed 10 - 9.

Examples

Input

1 3


Output

1.0000000000


Input

2 1


Output

2.3333333333


Input

10 2


Output

15.9380768924

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import static java.lang.Math.*;
import java.math.BigInteger;
import static java.math.BigInteger.*;
import static java.util.Arrays.*;
import javax.xml.ws.Holder;



//<editor-fold defaultstate="collapsed" desc="Main">
public class Task{
// https://netbeans.org/kb/73/java/editor-codereference_ru.html#display
    private void run() {
        try {
            Locale.setDefault(Locale.US);
        } catch (Exception e) {
        }
        boolean oj = true;
        try {
            oj = System.getProperty("MYLOCAL") == null;
        } catch (Exception e) {
        }

        if (oj) {
            sc = new FastScanner(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
        } else {
            try {
                sc = new FastScanner(new FileReader("input.txt"));
                out = new PrintWriter(new FileWriter("output.txt"));
            } catch (IOException e) {
                MLE();
            }
        }
        Solver s = new Solver();
        s.sc = sc;
        s.out = out;
        s.solve();
        if (!oj) {
            err.println("Time: " + (System.currentTimeMillis() - timeBegin) / 1e3);
            err.printf("Mem: %d\n", (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20);
        }
        out.flush();
    }

    private void show(int[] arr) {
        for (int v : arr) {
            err.print(" " + v);
        }
        err.println();
    }

    public static void exit() {
        err.println("Time: " + (System.currentTimeMillis() - timeBegin) / 1e3);
        out.flush();
        out.close();
        System.exit(0);
    }

    public static void MLE() {
        int[][] arr = new int[1024 * 1024][];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = new int[1024 * 1024];
        }
    }

    public static void main(String[] args) {
        new Task().run();
    }

    static long timeBegin = System.currentTimeMillis();
    static FastScanner sc;
    static PrintWriter out;
    static PrintStream err = System.err;
}
//</editor-fold>

//<editor-fold defaultstate="collapsed" desc="FastScanner">
class FastScanner {

    BufferedReader br;
    StringTokenizer st;

    FastScanner(InputStreamReader reader) {
        br = new BufferedReader(reader);
        st = new StringTokenizer("");
    }

    String next() {
        while (!st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException ex) {
                Task.MLE();
            }
        }
        return st.nextToken();
    }

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

    long nextLong() {
        return Long.parseLong(next());
    }
    double nextDouble() {
        return Double.parseDouble(next());
    }
}
//</editor-fold>

class Solver {
    void ass(boolean OK) { if(!OK)Task.MLE(); }

    FastScanner sc;
    PrintWriter out;
    static PrintStream err = System.err;

    final int maxT = (int)1e3;
    int maxN, k;
    double[] dp0, dp1;
    
    void solve(){
        maxN = sc.nextInt();
        k = sc.nextInt();
        dp0 = new double[maxT+1];
        dp1 = new double[maxT+1];
        
        for (int id = maxN-1; 0 <=id; --id) {
            for (int t = 1; t+1 <= maxT; t++) {
                double ans, sum = 0;
                sum = t * dp1[t] + (t+1.0)*t/2 + t + dp1[t+1];
                ans = (1-1.0/k) * dp1[t] + 1.0/k/(t+1)*sum;
                dp0[t] = ans;
            }
            System.arraycopy( dp0, 0, dp1, 0, dp0.length );
            fill( dp0, 0.0 );
        } 
        out.printf( "%.20f\n", k * dp1[1] );
    }

}