Problem B
A Rational Sequence 2

A sequence of positive rational numbers is defined as follows:

An infinite full binary tree labeled by positive rational numbers is defined by:

• The label of the root is $1/1$.

• The left child of label $p/q$ is $p/(p+q)$.

• The right child of label $p/q$ is $(p+q)/q$.

The top of the tree is shown in the following figure:

The sequence is defined by doing a level order (breadth first) traversal of the tree (indicated by the light dashed line). So that:

Write a program which finds the value of $n$ for which $F(n)$ is $p/q$ for inputs $p$ and $q$.

Input

The first line of input contains a single integer $P$, $(1 \le P \le 1000)$, which is the number of data sets that follow. Each data set should be processed identically and independently. Each data set consists of a single line of input. It contains the data set number, $K$, a single space, the numerator, $p$, a forward slash (/) and the denominator, $q$, of the desired fraction.

Output

For each data set there is a single line of output. It contains the data set number, $K$, followed by a single space which is then followed by the value of $n$ for which $F(n)$ is $p/q$. Inputs will be chosen so $n$ will fit in a $32$-bit integer.

4
1 1/1
2 1/3
3 5/2
4 2178309/1346269

1 1
2 4
3 11
4 1431655765