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>
inline int gd(int x) {
  int s = 0;
  for (; !(x & 1); x >>= 1) s++;
  return s;
}
double s[201][201];
int main() {
  int x, k, p_i;
  scanf("%d %d %d", &x, &k, &p_i);
  double p = (double)p_i / 100, q = 1 - p;
  for (register int i = 0; i <= k; i++) s[0][i] = gd(x + i);
  for (register int j = 1; j <= k; j++) {
    for (register int i = 0; i <= k; i++) {
      double s0 = 0, qa = 1.0;
      for (register int a = 0; a <= j - 1; a++) {
        if (!((a + i) & 1)) {
          int d = (a + i) >> 1;
          s0 += p * qa * (1 + s[j - 1 - a][d]);
        }
        qa *= q;
      }
      s0 += gd(x + j + i) * qa;
      s[j][i] = s0;
    }
  }
  printf("%0.10f\n", s[k][0]);
  return 0;
}