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and the day is not yet over

While training in Holodeck 3, Mr. Worf fires a phaser from one corner at an angle of 45 degrees to both walls, and parallel to the floor. Unfortunately, a fluctuation in one of the power conduit modulators makes all the walls into perfect mirrors, reflecting all phaser blasts in zero time and with no loss in speed. (In particular, a the phaser blast doubles back on itself if it hits a corner.)

The holodeck is a perfect rectangle n HUgif wide by k HU long. It takes 1 nanosecond to cross HU of space. The question: what is the length of time between Worf firing the phaser and the time that he gets stunned? (The holodeck safeties are also disengaged by the accident, so that he really does get stunned.) For the sake of simplicity, Worf is shrunk to take up zero width and breadth, and the tip of his phaser is positioned exactly in the corner. Also, on its return trip the phaser blast passes through the phaser and stuns Worf.

Input: The input to your program is a positive integer d, followed by d data sets. Each data set consists of positive integers n and k, respectively.

Output: The output for each data set should be the number of nanoseconds before Mr. Worf gets blasted. The answer for each data set will always be less than 2000000.

Sample input: (Editor's note: many people noticed that there are really only two data sets present, and so the "3" here should really be "2". Sorry!)

1 1
6 12

Corresponding sample output:


The game of the name: My favourite Worf quote is ``It is a good day to die and the day is not yet over''.

David Neto
Thu Jan 9 19:12:26 EST 1997