E. Valera and Number
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Valera is a coder. Recently he wrote a funny program. The pseudo code for this program is given below:

//input: integers x, k, pa = 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