E. Valera and Numbertime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputValera 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?InputThe first line of the input contains three integers x, k, p (1 ≤ x ≤ 109; 1 ≤ k ≤ 200; 0 ≤ p ≤ 100).OutputPrint the required expected value. Your answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.ExamplesInput1 1 50Output1.0000000000000Input5 3 0Output3.0000000000000Input5 3 25Output1.9218750000000NoteIf the concept of expected value is new to you, you can read about it by the link: http://en.wikipedia.org/wiki/Expected_value
Input1 1 50
Output1.0000000000000
['bitmasks', 'dp', 'math', 'probabilities', '*2400']