Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Wizards and Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn some country live wizards. They love playing with numbers.

The blackboard has two numbers written on it — *a* and *b*. The order of the numbers is not important. Let's consider *a* ≤ *b* for the sake of definiteness. The players can cast one of the two spells in turns:

- Replace
*b*with*b*-*a*^{k}. Number*k*can be chosen by the player, considering the limitations that*k*> 0 and*b*-*a*^{k}≥ 0. Number*k*is chosen independently each time an active player casts a spell. - Replace
*b*with*b**mod**a*.

If *a* > *b*, similar moves are possible.

If at least one of the numbers equals zero, a player can't make a move, because taking a remainder modulo zero is considered somewhat uncivilized, and it is far too boring to subtract a zero. The player who cannot make a move, loses.

To perform well in the magic totalizator, you need to learn to quickly determine which player wins, if both wizards play optimally: the one that moves first or the one that moves second.

Input

The first line contains a single integer *t* — the number of input data sets (1 ≤ *t* ≤ 10^{4}). Each of the next *t* lines contains two integers *a*, *b* (0 ≤ *a*, *b* ≤ 10^{18}). The numbers are separated by a space.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Output

For any of the *t* input sets print "First" (without the quotes) if the player who moves first wins. Print "Second" (without the quotes) if the player who moves second wins. Print the answers to different data sets on different lines in the order in which they are given in the input.

Examples

Input

4

10 21

31 10

0 1

10 30

Output

First

Second

Second

First

Note

In the first sample, the first player should go to (11,10). Then, after a single move of the second player to (1,10), he will take 10 modulo 1 and win.

In the second sample the first player has two moves to (1,10) and (21,10). After both moves the second player can win.

In the third sample, the first player has no moves.

In the fourth sample, the first player wins in one move, taking 30 modulo 10.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/31/2021 16:30:17 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|