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 dp[2][256] = {{0}};
int main() {
  int i, j;
  int x, k, p;
  int r;
  int yn;
  double ans = 0, ans2;
  double pd, pp;
  int next = 1;
  srand(time(NULL));
  scanf("%d %d %d", &x, &k, &p);
  pd = (double)p / 100;
  pp = (double)(100 - p) / 100;
  dp[0][0] = 1;
  for (i = 0; i < k; i++) {
    dp[next][0] = 0;
    for (j = 0; j < 255; j++) {
      dp[next][j + 1] = dp[1 - next][j] * pp;
    }
    for (j = 0; j < 255; j += 2) {
      ans += dp[1 - next][j] * pd;
      dp[next][j / 2] += dp[1 - next][j] * pd;
    }
    next = 1 - next;
  }
  for (i = 0; i < 255; i++) {
    r = i + x;
    while (r % 2 == 0) {
      r /= 2;
      ans += dp[1 - next][i];
    }
  }
  printf("%lf", ans);
  return 0;
}