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 x, k;
double p;
int neo = 0;
double memo[210][250][1 << 8][2];
bool calc[210][250][1 << 8][2];
double solve(int sp, int ez, int mask, int lead) {
  if (sp == k + 1) {
    int res = 0;
    if (mask == 0)
      res = 8;
    else {
      while (mask % 2 == 0) {
        res++;
        mask /= 2;
        if (mask == 0) break;
      }
    }
    if (lead == 0) {
      if (res == 8) return ez + 8.0;
    }
    return (double)res;
  }
  if (calc[sp][ez][mask][lead]) return memo[sp][ez][mask][lead];
  calc[sp][ez][mask][lead] = 1;
  double cur = 0;
  int fs = !!(mask & (1 << 7));
  if (lead == 0) {
    if (fs == 1)
      cur = cur + p * solve(sp + 1, 1, (mask << 1) % (1 << 8), 1);
    else
      cur = cur + p * solve(sp + 1, ez + 1, (mask << 1) % (1 << 8), 0);
    if (mask == (1 << 8) - 1)
      cur = cur + (1 - p) * solve(sp + 1, 1, 0, 1);
    else
      cur = cur + (1 - p) * solve(sp + 1, ez, mask + 1, 0);
  } else {
    if (fs == 1)
      cur = cur + p * solve(sp + 1, ez + 1, (mask << 1) % (1 << 8), 1);
    else
      cur = cur + p * solve(sp + 1, 1, (mask << 1) % (1 << 8), 0);
    if (mask == (1 << 8) - 1)
      cur = cur + (1 - p) * solve(sp + 1, ez, 0, 0);
    else
      cur = cur + (1 - p) * solve(sp + 1, ez, mask + 1, 1);
  }
  return memo[sp][ez][mask][lead] = cur;
}
int main() {
  cin >> x >> k >> p;
  p = p / 100.0;
  int premask = x % (1 << 8);
  x = x / (1 << 8);
  int nx = x % 2;
  while (x % 2 == nx) {
    neo++;
    x /= 2;
    if (x == 0) break;
  }
  cout << fixed << setprecision(9) << solve(1, neo, premask, nx) << "\n";
}