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 vis[220][220];
double dp[220][220], prob;
int x, k, p;
double rec(int moresteps, int add) {
  if (vis[moresteps][add]) return dp[moresteps][add];
  vis[moresteps][add] = 1;
  double &ret = dp[moresteps][add];
  if (moresteps == 0) {
    int yolo = x + add;
    while (yolo % 2 == 0) yolo /= 2, ret++;
    return ret;
  }
  if (add % 2 == 0) ret += prob * (1.0 + rec(moresteps - 1, add / 2));
  ret += (1.0 - prob) * (rec(moresteps - 1, add + 1));
  return ret;
}
int main() {
  cin >> x >> k >> p;
  prob = (double)p / 100.0;
  printf("%.12lf\n", rec(k, 0));
  return 0;
}