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;
double p;
double dp1[407];
double dp2[407];
int main() {
  scanf("%d%d%lf", &x, &k, &p);
  for (int i = 0; i < k + 1; i++) {
    for (int j = x + i; j % 2 == 0; j /= 2) {
      dp1[i]++;
    }
  }
  bool flag = true;
  for (int i = 0; i < k; i++) {
    if (flag) {
      memset(dp2, 0, sizeof(dp2));
      for (int j = 0; j < k + 1; j++) {
        dp2[j * 2] += (dp1[j] + 1) * (p / 100);
        dp2[j] += dp1[j + 1] * (100 - p) / 100;
      }
      flag = false;
    } else {
      memset(dp1, 0, sizeof(dp1));
      for (int j = 0; j < k + 1; j++) {
        dp1[j * 2] += (dp2[j] + 1) * (p / 100);
        dp1[j] += dp2[j + 1] * (100 - p) / 100;
      }
      flag = true;
    }
  }
  if (flag) {
    printf("%.13lf\n", dp1[0]);
  } else {
    printf("%.13lf\n", dp2[0]);
  }
  return 0;
}