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>
double s[201][201];
int zeros(int x) {
  int s = 0;
  while ((x & 1) == 0) {
    s++;
    x = x >> 1;
  }
  return s;
}
int main() {
  int x, kmax, pint;
  scanf("%d %d %d", &x, &kmax, &pint);
  double p = pint / 100.0;
  double q = 1 - p;
  for (int da = 0; da <= kmax; da++) {
    s[0][da] = zeros(x + da);
  }
  for (int k = 1; k <= kmax; k++) {
    for (int da = 0; da <= kmax; da++) {
      double s0 = 0;
      double qa = 1.0;
      for (int a = 0; a <= k - 1; a++) {
        if ((a + da) % 2 == 0) {
          int da2 = (a + da) / 2;
          s0 += p * qa * (1 + s[k - 1 - a][da2]);
        } else {
        }
        qa *= q;
      }
      s0 += zeros(x + k + da) * qa;
      s[k][da] = s0;
    }
  }
  printf("%0.10f\n", s[kmax][0]);
}