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 n, k, p;
int read() {
  int s = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    s = s * 10 + ch - '0';
    ch = getchar();
  }
  return s * f;
}
double dp[500][500];
int main() {
  n = read(), k = read(), p = read();
  double p1 = 1.0 * p / 100, p2 = 1.0 - p1;
  for (int i = 0; i <= k; ++i) {
    for (int j = n + i; (j & 1) == 0; j >>= 1) {
      dp[0][i] += 1.0;
    }
  }
  for (int i = 0; i < k; ++i) {
    for (int j = 0; j <= k; ++j) {
      if (j != 0) dp[i + 1][j - 1] += p2 * dp[i][j];
      if (j * 2 <= k) dp[i + 1][j * 2] += p1 * (dp[i][j] + 1);
    }
  }
  printf("%.10lf", dp[k][0]);
}