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 INF = 2e9 + 9;
long long x;
double p, dp[205][405];
bool usd[205][405];
double f(int i, int j) {
  if (i == 0) {
    long long n = x + (long long)j;
    int cnt = 0;
    while (n % 2 == 0) {
      n /= 2;
      cnt++;
    }
    return (double)cnt;
  }
  if (usd[i][j]) return dp[i][j];
  if (j % 2) {
    usd[i][j] = 1;
    return dp[i][j] = (1.0 - p) * f(i - 1, j + 1);
  } else {
    usd[i][j] = 1;
    return dp[i][j] = p * (f(i - 1, j / 2) + 1) + (1.0 - p) * f(i - 1, j + 1);
  }
}
int main() {
  int k;
  cin >> x >> k >> p;
  memset(usd, 0, sizeof(usd));
  p /= 100.0;
  printf("%.12lf\n", f(k, 0));
  return 0;
}