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;
double dp[220][220];
int n, k;
double p;
int calc(int k) {
  int ret = 0;
  while (k % 2 == 0) {
    k /= 2;
    ret++;
  }
  return ret;
}
int main() {
  scanf("%d%d%lf", &n, &k, &p);
  p /= 100;
  for (int i = 0; i <= k; ++i) dp[0][i] = calc(n + i);
  for (int t = 1; t <= k; ++t) {
    for (int z = 0; z <= k; ++z) {
      if (z % 2 == 0) dp[t][z] += p * (dp[t - 1][z / 2] + 1);
      if (z + 1 <= k) dp[t][z] += (1 - p) * (dp[t - 1][z + 1]);
    }
  }
  printf("%.12lf\n", dp[k][0]);
  return 0;
}