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 int N = 250 + 7;
const int inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-10;
const double PI = acos(-1);
template <class T, class S>
inline void add(T &a, S b) {
  a += b;
  if (a >= mod) a -= mod;
}
template <class T, class S>
inline void sub(T &a, S b) {
  a -= b;
  if (a < 0) a += mod;
}
template <class T, class S>
inline bool chkmax(T &a, S b) {
  return a < b ? a = b, true : false;
}
template <class T, class S>
inline bool chkmin(T &a, S b) {
  return a > b ? a = b, true : false;
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int x, k, p;
double dp[2][250][1 << 9];
double p1, p2;
double (*f)[1 << 9] = dp[0];
double (*g)[1 << 9] = dp[1];
inline int getLow(int mask) {
  for (int i = 0;; i++)
    if (mask >> i & 1) return i;
}
void print(int x, int cnt) {
  if (!cnt) return;
  print(x >> 1, cnt - 1);
  printf("%d", x & 1, cnt - 1);
}
int main() {
  scanf("%d%d%d", &x, &k, &p);
  p1 = 1.0 * p / 100;
  p2 = 1 - p1;
  int c = 0, mask = (x & 511);
  if (mask) {
    for (int i = 9;; i++) {
      if (x >> i & 1)
        c++;
      else
        break;
    }
  } else {
    c = getLow(x);
  }
  f[c][mask] = 1;
  for (int o = 0; o < k; o++) {
    swap(f, g);
    for (int i = 0; i <= 240; i++)
      for (int mask = 0; mask < (1 << 9); mask++) f[i][mask] = 0;
    for (int i = 0; i < 240; i++) {
      for (int mask = 0; mask < (1 << 9); mask++) {
        if (mask) {
          if (mask + 1 == (1 << 9)) {
            f[i + 9][0] += g[i][mask] * p2;
          } else {
            f[i][mask + 1] += g[i][mask] * p2;
          }
          int nmask = (mask << 1) & 511;
          int bit = mask >> 8 & 1;
          if (nmask) {
            if (bit) {
              f[i + 1][nmask] += g[i][mask] * p1;
            } else {
              f[0][nmask] += g[i][mask] * p1;
            }
          } else {
            f[9][0] += g[i][mask] * p1;
          }
        } else {
          f[0][1] += g[i][mask] * p2;
          f[i + 1][0] += g[i][mask] * p1;
        }
      }
    }
  }
  double ans = 0;
  for (int i = 0; i <= 240; i++) {
    for (int mask = 0; mask < (1 << 9); mask++) {
      if (mask) {
        ans += getLow(mask) * f[i][mask];
      } else {
        ans += i * f[i][mask];
      }
    }
  }
  printf("%.12f\n", ans);
  return 0;
}