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;
const int MAXN = 2e2 + 10;
double dp[MAXN][MAXN], pb;
bool vis[MAXN][MAXN];
int x;
double solve(int steps, int add) {
  if (vis[steps][add]) return dp[steps][add];
  vis[steps][add] = true;
  double& ret = dp[steps][add] = 0.00;
  if (steps == 0) {
    int num = x + add;
    while (num % 2 == 0) {
      ret++;
      num /= 2;
    }
  } else {
    if (add % 2 == 0) ret = pb * (1 + solve(steps - 1, add / 2));
    ret += (1.00 - pb) * (solve(steps - 1, add + 1));
  }
  return ret;
}
int main() {
  int steps, p;
  cin >> x >> steps >> p;
  pb = p * 0.01;
  printf("%.9lf\n", solve(steps, 0));
  return 0;
}