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 main(void) {
  int orig, k, perc;
  scanf("%d %d %d", &orig, &k, &perc);
  double p = perc / 100.;
  const int MAXN = 213;
  static double dp[MAXN][MAXN];
  for (int x = (0); x < (k + 1); ++x)
    for (int a = (0); a < (k + 1); ++a) {
      if (x == 0) {
        int s = 0;
        for (int tmp = orig + a; tmp % 2 == 0; tmp /= 2) ++s;
        dp[x][a] = s;
      } else {
        dp[x][a] += (1 - p) * dp[x - 1][a + 1];
        if (a % 2 == 0) dp[x][a] += p * (1 + dp[x - 1][a / 2]);
      }
    }
  printf("%.9lf\n", dp[k][0]);
  return 0;
}