CF441E.Valera and Number

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?

瓦列拉是一名程序员。最近他编写了一个有趣的程序。该程序的伪代码如下所示：

// 输入：整数 x、k、p
a = x;
for(step = 1; step <= k; step = step + 1){
rnd = [从 1 到 100 中均匀随机选取的整数];
if(rnd <= p)
a = a * 2;
else
a = a + 1;
}

s = 0;

while(a 除以 2 的余数等于 0){
a = a / 2;
s = s + 1;
}

现在瓦列拉想知道：给定参数 x、k 和 p，最终得到的数 s 的期望值是多少？

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

输入的第一行包含三个整数 $x$、$k$、$p$（$1 \le x \le 10^9$；$1 \le k \le 200$；$0 \le p \le 100$）。

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

输出所需的期望值。只要您的答案的绝对误差或相对误差不超过 $10^{-6}$，即视为正确。

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

如果期望值的概念对你来说是新的，你可以通过以下链接了解它：

http://en.wikipedia.org/wiki/Expected_value