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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 310;
int x, k;
double p, q, f[N][N];
int main() {
  scanf("%d%d%lf", &x, &k, &p);
  p /= 100;
  q = 1.0 - p;
  for (int i = 0; i <= k; ++i) f[0][i] = (double)__builtin_ctz(x + i);
  for (int i = 1; i <= k; ++i)
    for (int j = 0; j <= k; ++j) {
      f[i][j] += f[i - 1][j + 1] * q;
      if (j * 2 <= k) f[i][j << 1] += (f[i - 1][j] + 1.0) * p;
    }
  printf("%.15lf\n", f[k][0]);
  return 0;
}