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>
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
using ll = long long;
using db = long double;
using ii = pair<int, int>;
const int N = 1e6 + 5, LG = 19, MOD = 998244353;
const int SQ = 225;
const long double EPS = 1e-7;
int x, k;
double p, dp[205][205];
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> x >> k >> p;
  p /= 100.0;
  for (int i = 0; i < k + 1; i++) {
    dp[0][i] = __builtin_ctz(x + i);
  }
  for (int i = 1; i < k + 1; i++) {
    for (int j = 0; j < k + 1; j++) {
      if (j * 2 <= k) dp[i][j + j] += (dp[i - 1][j] + 1) * p;
      if (j - 1 >= 0) dp[i][j - 1] += (dp[i - 1][j]) * (1.0 - p);
    }
  }
  cout << fixed << setprecision(6) << dp[k][0] << '\n';
  return 0;
}