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 long long linf = 1e18 + 5;
const int mod = (int)1e9 + 7;
const int logN = 17;
const int inf = 1e9;
const int N = 1e3 + 50;
int x, k, p;
double dp[N][N], o;
double f(int x, int y) {
  if (y == 0) {
    x += ::x;
    int t = 0;
    while (x % 2 == 0) {
      t++;
      x /= 2;
    }
    return t;
  }
  double &r = dp[x][y];
  if (r != -1) return r;
  return r = (f(x / 2, y - 1) + 1) * o * !(x & 1) + f(x + 1, y - 1) * (1 - o);
}
int main() {
  scanf("%d %d %d", &x, &k, &p);
  o = p / 100.0;
  int ans = 0;
  for (int i = 0; i <= 1023; i++)
    for (int j = 0; j <= k + 1; j++) dp[i][j] = -1;
  printf("%.12lf\n", f(0, k));
  return 0;
}