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 Maxk = 205;
int x, k, p;
double mp;
double prob[Maxk][Maxk][Maxk];
double res;
int Get(int x) {
  int res = 0;
  while (x % 2 == 0) {
    res++;
    x /= 2;
  }
  return res;
}
int main() {
  scanf("%d %d %d", &x, &k, &p);
  mp = double(p) / 100;
  prob[0][0][0] = 1;
  for (int i = 0; i < k; i++)
    for (int j = 0; j + 1 < Maxk; j++)
      for (int l = 0; l + 1 < Maxk; l++) {
        if (l % 2 == 0) {
          prob[i + 1][j + 1][l / 2] += mp * prob[i][j][l];
          res += mp * prob[i][j][l];
        }
        prob[i + 1][j][l + 1] += (1.0 - mp) * prob[i][j][l];
      }
  for (int j = 0; j < Maxk; j++)
    for (int l = 0; l < Maxk; l++) res += prob[k][j][l] * Get(x + l);
  printf("%.13lf\n", res);
  return 0;
}