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 xx[4] = {0, 0, 1, -1};
int yy[4] = {1, -1, 0, 0};
int x, k, p;
double f[205][256][2][250];
int getbit(int x, int i) { return (x >> (i)) & 1; }
int calc(int mask, int b, int cnt) {
  if (mask == 0) {
    if (b == 0) {
      return 7 + cnt + 1;
    } else
      return 8;
  } else {
    for (int i = (0), _b = (7); i <= _b; i++)
      if (getbit(mask, i) == 1) return i;
  }
}
int main() {
  scanf("%d%d%d", &x, &k, &p);
  int r = (1 << 8) - 1;
  int cnt = 0;
  for (int i = (8), _b = (32); i <= _b; i++)
    if (getbit(x, i) == getbit(x, 8))
      cnt++;
    else
      break;
  f[0][x & r][getbit(x, 8)][cnt] = 1;
  for (int i = (0), _b = (k - 1); i <= _b; i++)
    for (int mask = (0), _b = (r); mask <= _b; mask++)
      for (int b = (0), _b = (1); b <= _b; b++)
        for (int cnt = (1), _b = (32 + 200); cnt <= _b; cnt++)
          if (f[i][mask][b][cnt] != 0) {
            int c = getbit(mask, 7);
            int cnt2;
            if (c == b)
              cnt2 = cnt + 1;
            else
              cnt2 = 1;
            f[i + 1][(mask << 1) & r][c][cnt2] +=
                f[i][mask][b][cnt] * double(p) / 100;
            if (mask == r) {
              if (b == 0) {
                c = 1;
                cnt2 = 1;
              } else {
                c = 0;
                cnt2 = cnt;
              }
            } else {
              c = b;
              cnt2 = cnt;
            }
            f[i + 1][(mask + 1) & r][c][cnt2] +=
                f[i][mask][b][cnt] * (double(100 - p)) / 100;
          }
  double res = 0;
  for (int mask = (0), _b = (r); mask <= _b; mask++)
    for (int b = (0), _b = (1); b <= _b; b++)
      for (int cnt = (1), _b = (32 + 200); cnt <= _b; cnt++)
        if (f[k][mask][b][cnt] != 0)
          res += f[k][mask][b][cnt] * calc(mask, b, cnt);
  printf("%.9lf\n", res);
}