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;
const int maxn = 1e6 + 7;
long long read() {
  long long res = 0, f = 1;
  char c = getchar();
  while (!isdigit(c) && c != '-') c = getchar();
  if (c == '-') f = -1, c = getchar();
  while (isdigit(c)) res = (res << 1) + (res << 3) + c - 48, c = getchar();
  return res * f;
}
int n, k;
double p;
double f[310][310];
int main() {
  n = read(), k = read(), p = 1.0 * read() / 100;
  for (int i = 0; i <= k; i++) {
    for (int j = n + i; j % 2 == 0; j /= 2) {
      f[0][i]++;
    }
  }
  for (int i = 0; i < k; i++) {
    for (int j = 0; j <= k; j++) {
      if (j) f[i + 1][j - 1] += (1.0 - p) * f[i][j];
      if (j * 2 <= k) f[i + 1][j * 2] += p * (f[i][j] + 1);
    }
  }
  printf("%.7f\n", f[k][0]);
  return 0;
}