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;
float p, dp[201][201];
int x;
float foo(int steps, int add) {
  if (dp[steps][add] != -1) return dp[steps][add];
  float ret = 0;
  if (!steps) {
    int n = x + add;
    while (n % 2 == 0) {
      ret++;
      n /= 2;
    }
  } else {
    if (add % 2 == 0) ret += p * (1 + foo(steps - 1, add / 2));
    ret += (1 - p) * foo(steps - 1, add + 1);
  }
  dp[steps][add] = ret;
  return ret;
}
int main() {
  int k;
  for (int i = 0; i < 201; i++)
    for (int j = 0; j < 201; j++) dp[i][j] = -1;
  cin >> x >> k >> p;
  p /= 100.;
  printf("%.10f\n", foo(k, 0));
}