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;
double F[210][235][256][2];
int a, b, c;
inline int bitcnt(int x, int y) {
  int s = 0;
  while (x && (x & 1) == y) ++s, x >>= 1;
  return s;
}
double get(int x, int y, int k, int p) {
  if (x == b)
    if (!k)
      return (p ? 0 : y) + 8;
    else
      return bitcnt(k, 0);
  if (F[x][y][k][p] > -0.5) return F[x][y][k][p];
  double s =
      get(x + 1, (p == (k > 127)) ? y + 1 : 1, (k << 1) & 255, k > 127) * c;
  if (k < 255)
    s += get(x + 1, y, k + 1, p) * (100 - c);
  else
    s += get(x + 1, p ? y : 1, 0, !p) * (100 - c);
  F[x][y][k][p] = s / 100;
  return F[x][y][k][p];
}
int main() {
  iostream::sync_with_stdio(false);
  cin.tie(NULL);
  int x, k = 0;
  cin >> a >> b >> c;
  fill(F[0][0][0], F[b][0][0], -1.0);
  cout << fixed << get(0, bitcnt(a >> 8, (a >> 8) & 1), a & 255, (a >> 8) & 1);
  return 0;
}