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;
using ll = long long;
double p;
bool in_memo[200 + 1][230 + 1][2][1 << 8];
double memo[200 + 1][230 + 1][2][1 << 8];
double E(int k, int lead_count, bool lead_parity, int mask) {
  double& ans = memo[k][lead_count][lead_parity][mask];
  if (not in_memo[k][lead_count][lead_parity][mask]) {
    if (k == 0) {
      ans = mask ? __builtin_ctz(mask) : 8 + (lead_parity ? 0 : lead_count);
    } else {
      ans = p / 100 *
                E(k - 1,
                  bool((mask & (1 << 7)) >> 7) == lead_parity ? lead_count + 1
                                                              : 1,
                  (mask & (1 << 7)) >> 7, (mask * 2) & 0b11111111) +
            (100 - p) / 100 *
                E(k - 1,
                  mask == 0b11111111 ? (lead_parity ? lead_count : 1)
                                     : lead_count,
                  lead_parity ^ (mask == 0b11111111), (mask + 1) & 0b11111111);
    }
    in_memo[k][lead_count][lead_parity][mask] = true;
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int x, k;
  cin >> x >> k >> p;
  memset(in_memo, false, sizeof in_memo);
  cout << fixed << setprecision(7)
       << E(k, __builtin_ctz((x >> 8) & 1 ? (x >> 8) + 1 : x >> 8),
            (x >> 8) & 1, x & 0b11111111)
       << '\n';
  return 0;
}