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?

The first line of the input contains three integers x, k, p (1 ≤ x ≤ 10⁹; 1 ≤ k ≤ 200; 0 ≤ p ≤ 100).

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