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;
template <typename T>
inline void read(T &x) {
  x = 0;
  char c = getchar(), f = 0;
  for (; c < 48 || c > 57; c = getchar())
    if (!(c ^ 45)) f = 1;
  for (; c >= 48 && c <= 57; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
  f ? x = -x : x;
}
const double eps = 1e-10;
int X, K;
double dp[205][205], p, rs = 0;
int main() {
  read(X), read(K), scanf("%lf", &p), p /= 100;
  for (int i = 0; i <= K; i++)
    for (int j = X + i; !(j & 1); j >>= 1, dp[0][i]++)
      ;
  for (int i = 0; i < K; i++)
    for (int j = 0; j <= K; j++)
      (j ? dp[i + 1][j - 1] += dp[i][j] * (1 - p) : p),
          (j * 2 <= K ? dp[i + 1][j * 2] += (dp[i][j] + 1) * p : p);
  return printf("%.10lf\n", dp[K][0]), 0;
}