SP9034 TOHU - Help Tohu

Description

Tohu wants to enter Moscow State University, and he must pass the math exam. He does not know math, and asks you to help him. The problem is to find the sum ![](http://www.spoj.com/content/cyclops:tohu_1.png "S_n = a_1 + a_2 + \ldots + a_n") of the sequence ![](http://www.spoj.com/content/cyclops:tohu_2.png "\left{ a_n \right}") on condition ![](http://www.spoj.com/content/cyclops:tohu_3.png "\forall k \in \mathbb{N} : a_1 + 2a_2 + \ldots + ka_k = \frac{k+1}{k+2}")

Input Format

First line contains single integer T

Output Format

For each n output the value ![](http://www.spoj.com/content/cyclops:tohu_4.png "S_n") with 11 digits after decimal point.