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 f[1 << 8][234][2][204];
double F(int mask, int num, bool c, int cnt) {
  if (mask & 1 << 8) {
    mask -= 1 << 8;
    if (c) {
      c = 0;
    } else {
      c = 1;
      num = 1;
    }
  }
  double &ans = f[mask][num][c][cnt];
  if (ans != -1) return ans;
  if (cnt == k) {
    ans = 0;
    if (mask == 0)
      if (num)
        return ans = 8 + (1 - c) * num;
      else
        return 0;
    else {
      while (mask % 2 == 0) {
        mask /= 2;
        ans++;
      }
    }
    return ans;
  }
  ans = (100 - p) / 100.0 * F(mask + 1, num, c, cnt + 1);
  int nex = mask * 2, nc = c, nnum = num;
  if (nex & 1 << 8) {
    nex -= 1 << 8;
    if (nc)
      nnum++;
    else {
      nnum = 1;
      nc = 1;
    }
  } else {
    if (nc) {
      nc = 0;
      nnum = 1;
    } else
      nnum++;
    if (num == 0) nnum = 0;
  }
  ans += p / 100.0 * F(nex, nnum, nc, cnt + 1);
  return ans;
}
void MAIN() {
  for (int i = 0; i < (1 << 8); i++)
    for (int j = 0; j < (234); j++)
      for (int l = 0; l < (2); l++)
        for (int c = 0; c < (204); c++) f[i][j][l][c] = -1;
  cin >> x >> k >> p;
  int mask = (x & (1 << 8) - 1), num = 0, c = 0;
  x >>= 8;
  if (x % 2) {
    c = 1;
    while (x % 2) {
      num++;
      x /= 2;
    }
  } else {
    if (x)
      while (x % 2 == 0) {
        num++;
        x /= 2;
      }
  }
  cout.precision(10);
  cout << fixed << F(mask, num, c, 0);
}
int main() {
  ios::sync_with_stdio(false);
  MAIN();
}