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;
char B[1 << 16], *_S = B, *_T = B;
template <typename T>
T read(void) {
  register T f = 1, num = 0;
  char c = (_S == _T && (_T = (_S = B) + fread(B, 1, 1 << 16, stdin), _S == _T)
                ? EOF
                : *_S++);
  while (!isdigit(c)) {
    if (c == '-') f = -f;
    c = (_S == _T && (_T = (_S = B) + fread(B, 1, 1 << 16, stdin), _S == _T)
             ? EOF
             : *_S++);
  }
  while (isdigit(c))
    num = (num << 3) + (num << 1) + (c ^ 48),
    c = (_S == _T && (_T = (_S = B) + fread(B, 1, 1 << 16, stdin), _S == _T)
             ? EOF
             : *_S++);
  return f * num;
}
double f[2][305];
int main() {
  int x = read<int>(), k = read<int>();
  double p1 = read<int>() / 100.0, p2 = 1 - p1;
  for (register int i = 0; i <= k; i++)
    for (register int j = x + i; !(j & 1); j >>= 1) f[0][i]++;
  for (register int i = 0; i < k; i++) {
    bool thi = i & 1, tha = !thi;
    memset(f[tha], 0, sizeof(f[tha]));
    for (register int j = 0; j <= k; j++) {
      if (j) f[tha][j - 1] += p2 * f[thi][j];
      if ((j << 1) <= k) f[tha][j << 1] += p1 * (f[thi][j] + 1);
    }
  }
  printf("%.13lf\n", f[k & 1][0]);
  return 0;
}