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 $*x*, *k*, *p*$ ($1 ≤ *x* ≤ 10^{9}; 1 ≤ *k* ≤ 200; 0 ≤ *p* ≤ 100$).

Output

Print the required expected value. Your answer will be considered correct if the absolute or relative error doesn't exceed $10^{ - 6}$.

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