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;
int x, k, p;
double f[2][500];
inline int c(int x, int t = 0) {
  for (; ~x & 1; x >>= 1) ++t;
  return t;
}
int main() {
  scanf("%d%d%d", &x, &k, &p);
  for (int i = 0; i <= k; ++i) f[0][i] = c(x + i);
  for (int i = 0; i < k; ++i) {
    memset(f[1], 0, sizeof f[1]);
    for (int j = 0; j <= k; ++j) {
      f[1][j << 1] += (f[0][j] + 1) * (p / 100.);
      f[1][j] += f[0][j + 1] * (1 - p / 100.);
    }
    swap(f[0], f[1]);
  }
  printf("%.10lf\n", f[0][0]);
}