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, l, b, c, d;
double p, ans;
double f[205][256][2][255];
int main() {
  scanf("%d%d%lf", &x, &k, &p);
  p = p / 100.0;
  l = x & 255;
  x >>= 8;
  b = x & 1;
  if (x > 0) c = 1;
  x >>= 1;
  while (x) {
    if ((x & 1) == b)
      c++;
    else
      break;
    x >>= 1;
  }
  f[0][l][b][c] = 1.0;
  for (x = 0; x < k; x++)
    for (l = 0; l < 256; l++)
      for (b = 0; b <= 1; b++)
        for (c = 0; c <= 250; c++)
          if (f[x][l][b][c] > 0) {
            if ((l >> 7) == b)
              f[x + 1][(l << 1) & 255][l >> 7][c == 0 ? (l >= 128) : c + 1] +=
                  f[x][l][b][c] * p;
            else
              f[x + 1][(l << 1) & 255][l >> 7][c == 0 ? (l >= 128) : 1] +=
                  f[x][l][b][c] * p;
            if (l + 1 < 256)
              f[x + 1][l + 1][b][c] += f[x][l][b][c] * (1 - p);
            else if (b == 1)
              f[x + 1][0][0][c] += f[x][l][b][c] * (1 - p);
            else
              f[x + 1][0][1][1] += f[x][l][b][c] * (1 - p);
          }
  for (l = 0; l < 256; l++)
    for (b = 0; b <= 1; b++)
      for (c = 0; c <= 250; c++)
        if (f[k][l][b][c] > 0) {
          x = l;
          d = 0;
          while (x) {
            if (x & 1) break;
            d++;
            x >>= 1;
          }
          if (b == 0 && l == 0 && c > 0) d = c + 8;
          if (b == 1 && l == 0 && c > 0) d = 8;
          ans += f[k][l][b][c] * d;
        }
  printf("%.13lf\n", ans);
  return 0;
}