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;
int x, k, p;
double eht, dp[200 + 5][1 << 8][2][250 + 5];
string op;
int main() {
  cin >> x >> k >> p;
  eht = (p + 0.00) / 100.00;
  if (x <= 255)
    dp[0][x][0][0] = 1.00;
  else {
    int tmp = 8;
    while (((x >> tmp) & 1) == ((x >> 8) & 1)) tmp++;
    dp[0][x % 256][(x >> 8) & 1][tmp - 8] = 1.00;
  }
  double ans = 0.00;
  for (int i = 0; i < k; i++)
    for (int mask = 0; mask < (1 << 8); mask++)
      for (int last = 0; last <= 1; last++)
        for (int ted = 0; ted <= 250; ted++) {
          double &ret = dp[i][mask][last][ted];
          if (last != ((mask >> 7) & 1) || !ted)
            dp[i + 1][(mask << 1) % 256][mask >> 7][1] += (ret * eht);
          else
            dp[i + 1][(mask << 1) % 256][last][ted + 1] += (ret * eht);
          if (!mask % 2)
            dp[i + 1][mask ^ 1][last][ted] += (ret * (1.00 - eht));
          else {
            if (mask != 255)
              dp[i + 1][mask + 1][last][ted] += (ret * (1.00 - eht));
            else {
              if (last == 0)
                dp[i + 1][0][1][1] += (ret * (1.00 - eht));
              else
                dp[i + 1][0][0][ted] += (ret * (1.00 - eht));
            }
          }
        }
  for (int mask = 0; mask < (1 << 8); mask++)
    for (int last = 0; last < 2; last++)
      for (int ted = 0; ted <= 250; ted++) {
        double &ret = dp[k][mask][last][ted];
        int sefr = 0;
        if (mask == 0) {
          sefr = 8;
          if (last == 0) sefr += ted;
        } else {
          int u = mask;
          while (u % 2 == 0) {
            sefr++;
            u >>= 1;
          }
        }
        ans += (ret * (sefr + 0.00));
      }
  cout << fixed << setprecision(6) << ans << endl;
  return 0;
}