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 double eps(1e-50);
const int K = 2, L = 250, B = 8, S = 1 << B, Unknown = -1;
int x, k, p, table[S] = {};
double f[K][2][L][S] = {};
bool in[K][2][L][S] = {};
struct state {
  int l, t1, t2, s;
};
queue<state> q;
void init() {
  for (int i = 0; i < S; ++i)
    for (int t = 0; t < B; ++t)
      if ((i & (1 << t)) == 0)
        ++table[i];
      else
        break;
  scanf("%d%d%d", &x, &k, &p);
  int ls = x / S, p1 = ls % 2, p2 = 0;
  while (ls && ls % 2 == p1) {
    ++p2;
    ls /= 2;
  }
  f[0][p1][p2][x % S] = 1;
  in[0][p1][p2][x % S] = true;
  q.push((state){0, p1, p2, x % S});
}
void multi2(const state &start) {
  state end = {start.l + 1, start.s >> (B - 1), Unknown,
               (start.s << 1) & (S - 1)};
  end.t2 = start.t2 * (end.t1 == start.t1) + 1;
  double &from = f[start.l & 1][start.t1][start.t2][start.s];
  double &to = f[end.l & 1][end.t1][end.t2][end.s];
  if (in[end.l & 1][end.t1][end.t2][end.s] == 0) {
    q.push(end);
    in[end.l & 1][end.t1][end.t2][end.s] = true;
  }
  to += from * (p / 100.0);
}
void add1(const state &start) {
  state end = {start.l + 1, start.t1, Unknown, Unknown};
  if (start.s == S - 1) {
    end.t1 = !end.t1;
    if (end.t1 == 1)
      end.t2 = 1;
    else
      end.t2 = start.t2;
    end.s = 0;
  } else {
    end.t2 = start.t2;
    end.s = start.s + 1;
  }
  double &from = f[start.l & 1][start.t1][start.t2][start.s];
  double &to = f[end.l & 1][end.t1][end.t2][end.s];
  if (in[end.l & 1][end.t1][end.t2][end.s] == 0) {
    q.push(end);
    in[end.l & 1][end.t1][end.t2][end.s] = true;
  }
  to += from * ((100 - p) / 100.0);
}
inline int value(const state &now) {
  return (now.t1 == 0 && now.s == 0) ? now.t2 + 8 : table[now.s];
}
void work() {
  double expect = 0;
  while (!q.empty()) {
    state now = q.front();
    q.pop();
    in[now.l & 1][now.t1][now.t2][now.s] = false;
    double &p = f[now.l & 1][now.t1][now.t2][now.s];
    if (now.l == k) {
      expect += value(now) * p;
      continue;
    }
    if (p == 0) {
      continue;
    }
    multi2(now);
    add1(now);
    p = 0;
  }
  printf("%.13f\n", expect);
}
int main() {
  init();
  work();
  return 0;
}