The algorithm of Petya#3237
Two positive integers are written on the board. Peter repeatedly performs the following operation: he replaces the smaller of the two numbers with the arithmetic mean of these numbers, and the larger number remains unchanged. He continues this operation until the two numbers become equal. Free Pete from his exhausting work.
The first line of the input file contains the number of test cases, (1 \le t \le 100000).
Each test contains two positive integers and (1 \le a, b \le 2 \cdot 10^9).
For each test case output the answer to the problem. In the case of a non-integer result, output it as an irreducible fraction . If the algorithm will run forever, output .
Example 1