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 dp[205][2][250][256], P;
int vl[256];
int main() {
  scanf("%d%d%d", &x, &K, &p);
  double P = p * 1.0 / 100;
  int pre = x >> 8, suf = x & 255, v = pre & 1, cnt = 0;
  if (pre == 0)
    cnt = 1;
  else
    while ((pre & 1) == v) cnt++, pre >>= 1;
  dp[0][v][cnt][suf] = 1;
  vl[0] = 8;
  for (int i = 1; i < 256; i++) {
    int tmp = i;
    while (!(tmp & 1)) tmp >>= 1, vl[i]++;
  }
  for (int i = 1; i <= K; i++) {
    for (int j = 0; j < 2; j++) {
      for (int k = 0; k < i + 32; k++) {
        for (int l = 0; l < 255; l++) {
          dp[i][(l >> 7) & 1][((l >> 7) & 1) == j ? k + 1 : 1]
            [(l << 1) & 255] += dp[i - 1][j][k][l] * P;
          dp[i][j][k][l + 1] += dp[i - 1][j][k][l] * (1 - P);
        }
        dp[i][(255 >> 7) & 1][((255 >> 7) & 1) == j ? k + 1 : 1]
          [(255 << 1) & 255] += dp[i - 1][j][k][255] * P;
        if (j == 0)
          dp[i][1][1][0] += dp[i - 1][j][k][255] * (1 - P);
        else
          dp[i][0][k][0] += dp[i - 1][j][k][255] * (1 - P);
      }
    }
  }
  double ans = 0;
  for (int i = 1; i <= K + 32; i++) {
    for (int j = 1; j < 256; j++)
      ans += (dp[K][0][i][j] + dp[K][1][i][j]) * vl[j];
    ans += dp[K][0][i][0] * (8 + i);
    ans += dp[K][1][i][0] * 8;
  }
  printf("%.10lf\n", ans);
  return 0;
}