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[205][205][205], ans;
int i, j, k, X, K, P, now, t;
int main() {
  scanf("%d%d%d", &X, &K, &P);
  dp[0][0][0] = 1;
  for (i = 1; i <= K; i++)
    for (j = 0; j < i; j++)
      for (k = 0; k <= i; k++) {
        if (k % 2 == 0)
          dp[i][j + 1][k / 2] += dp[i - 1][j][k] * (P / 100.0);
        else
          ans += dp[i - 1][j][k] * (P / 100.0) * j;
        dp[i][j][k + 1] += dp[i - 1][j][k] * (1 - P / 100.0);
      }
  for (j = 0; j <= K; j++)
    for (k = 0; k <= K; k++) {
      now = k + X;
      t = 0;
      while (now % 2 == 0) {
        t++;
        now /= 2;
      }
      ans += dp[K][j][k] * (t + j);
    }
  printf("%.10f\n", ans);
  return 0;
}