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>
int main() {
  static double dp[201][201] = {0.};
  int n, k, a;
  scanf("%d %d %d", &n, &k, &a);
  double p = a / 100.;
  for (int i = 0; i <= k; i++) {
    for (int j = 0; j <= k; j++) {
      if (i == 0) {
        for (int x = n + j; x % 2 == 0; x /= 2) dp[0][j] += 1.0;
      } else {
        dp[i][j] += (dp[i - 1][j + 1] * (1 - p));
        if (j % 2 == 0) dp[i][j] += (p * (dp[i - 1][j / 2] + 1));
      }
    }
  }
  printf("%.10lf", dp[k][0]);
}