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 K = 205;
int x, k;
double p, f[K][K];
int cnt(int x) {
  int tot = 0;
  while (x % 2 == 0) tot++, x /= 2;
  return tot;
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> x >> k >> p;
  p /= 100.0;
  for (register int i = (0); i <= (k); ++i) f[0][i] = cnt(x + i);
  for (register int i = (1); i <= (k); ++i)
    for (register int j = (0); j <= (k); ++j) {
      f[i][j] += f[i - 1][j + 1] * (1.0 - p);
      if (2 * j <= k) f[i][2 * j] += (f[i - 1][j] + 1.0) * p;
    }
  cout << fixed << setprecision(10) << f[k][0] << '\n';
  return 0;
}