Problem: Valera is a coder. Recently he wrote a funny program. The pseudo code for this program is given below:
    
    
      
    //input: integers x, k, p  
    a = x;  
    for(step = 1; step <= k; step = step + 1){  
        rnd = [random integer from 1 to 100];  
        if(rnd <= p)  
            a = a * 2;  
        else  
            a = a + 1;  
    }  
      
    s = 0;  
      
    while(remainder after dividing a by 2 equals 0){  
        a = a / 2;  
        s = s + 1;  
    }  
      
    

Now Valera wonders: given the values x, k and p, what is the expected value of the resulting number s?

Input

The first line of the input contains three integers x, k, p (1 ≤ x ≤ 109; 1 ≤ k ≤ 200; 0 ≤ p ≤ 100).

Output

Print the required expected value. Your answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples

Input

1 1 50


Output

1.0000000000000


Input

5 3 0


Output

3.0000000000000


Input

5 3 25


Output

1.9218750000000

Note

If the concept of expected value is new to you, you can read about it by the link: 

http://en.wikipedia.org/wiki/Expected_value

Solution (in JAVA):

Solution:

import java.util.Arrays;
import java.util.Scanner;

public class E {
    static double DP[][][][];
    static double p;
    static int screen = (1 << 8) - 1;

    public static double get(int index, int mask, int ninth, int cnt) {
        if (index == 0) {
            int res = 0;
            while ((mask & 1) == 0 && res < 8) {
                res++;
                mask >>= 1;
            }
            if (res == 8 && ninth == 0)
                res += cnt;
            return res;
        }
        if (DP[index][mask][ninth][cnt] != -1)
            return DP[index][mask][ninth][cnt];
        double res = 0;
        int nextBit = (mask & (1 << 7)) == 0 ? 0 : 1;
        int nextCnt = nextBit == ninth ? (cnt + 1) : 1;
        int nextMask = (mask << 1);
        res += p * get(index - 1, nextMask & screen, nextBit, nextCnt);

        nextMask = mask + 1;
        nextBit = (nextMask & (1 << 8)) == 0 ? ninth : ((1 + ninth) & 1);
        nextCnt = nextBit == 0 || ninth == 1 ? cnt : 1;
        res += (1 - p) * get(index - 1, nextMask & screen, nextBit, nextCnt);
        return DP[index][mask][ninth][cnt] = res;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int x = in.nextInt();
        int k = in.nextInt();
        p = in.nextDouble() / 100;
        DP = new double[k + 1][1 << 8][2][250];
        for (int i = 0; i < DP.length; i++)
            for (int j = 0; j < DP[0].length; j++)
                for (int l = 0; l < DP[0][0].length; l++)
                    Arrays.fill(DP[i][j][l], -1);
        int mask = x & screen;
        int ninth = (x & (1 << 8)) == 0 ? 0 : 1;
        int cnt = 0;
        x >>= 8;
        while ((x & 1) == ninth && x > 0) {
            cnt++;
            x >>= 1;
        }
        System.out.println(get(k, mask, ninth, cnt));
    }
}