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;
double PI = acos(-1);
double EPS = 1e-7;
int INF = 1000000000;
int MOD = 1000000007;
int MAXINT = 2147483647;
long long INFLL = 1000000000000000000LL;
long long MAXLL = 9223372036854775807LL;
int mx[8] = {-1, 1, 0, 0, -1, -1, 1, 1};
int my[8] = {0, 0, -1, 1, -1, 1, -1, 1};
int x, k, p;
double per;
int lim = (1 << 8) - 1;
double dp[205][235][2][1 << 8];
bool vs[205][235][2][1 << 8];
double go(int pos, int cons, int t, int mask) {
  if (vs[pos][cons][t][mask]) return dp[pos][cons][t][mask];
  vs[pos][cons][t][mask] = 1;
  double &ret = dp[pos][cons][t][mask];
  ret = 0.0;
  if (pos == 0) {
    if (mask == 0) {
      if (t == 1)
        return ret = 8;
      else
        return ret = 8 + cons;
    } else {
      int co = 0;
      while (mask % 2 == 0) {
        co++;
        mask /= 2;
      }
      return ret = co;
    }
  }
  if (mask < lim) {
    ret += (1.0 - per) * go(pos - 1, cons, t, mask + 1);
  } else {
    if (t == 0)
      ret += (1.0 - per) * go(pos - 1, 1, 1, 0);
    else
      ret += (1.0 - per) * go(pos - 1, cons, 0, 0);
  }
  bool d = mask & (1 << 7);
  if (d) mask -= (1 << 7);
  if (d == t) {
    ret += per * go(pos - 1, cons + 1, d, 2 * mask);
  } else {
    ret += per * go(pos - 1, 1, d, 2 * mask);
  }
  return ret;
}
int main() {
  scanf("%d%d%d", &x, &k, &p);
  per = (double)p / 100.0;
  int mask = 0;
  int cons = 0;
  bool t = (x & (1 << 8));
  for (int(a) = (0); (a) <= (30); (a)++) {
    if (a <= 7) {
      if (x & (1 << a)) mask += (1 << a);
    } else {
      if (t && ((x & (1 << a)) > 0)) cons++;
      if (t && ((x & (1 << a)) == 0)) break;
      if (!t && ((x & (1 << a)) == 0)) cons++;
      if (!t && ((x & (1 << a)) > 0)) break;
    }
  }
  printf("%.10lf\n", go(k, cons, t, mask));
}