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 m, n;
double p, q, f[222][222];
int main() {
  cin >> m >> n >> p;
  p /= 100;
  q = 1 - p;
  for (int _r = n, i = 0; i <= _r; ++i)
    for (int j = m + i; j % 2 == 0; j /= 2) ++f[0][i];
  for (int _r = n, i = 0; i < _r; ++i)
    for (int _r = n, j = 0; j <= _r; ++j) {
      if (j) f[i + 1][j - 1] += q * f[i][j];
      if (j * 2 <= n) f[i + 1][j * 2] += p * (f[i][j] + 1);
    }
  cout << fixed << setprecision(20) << f[n][0];
}