409937: GYM103860 G Integer Game

Two players play a game of integers.

The game consists of $$$n$$$ positive integer sets and an integer $$$p$$$ greater than $$$1$$$. The $$$i$$$-th set $$$s_i$$$ initially contains all integers in the range $$$[l_i, r_i]$$$.

The first player makes the first move, then players alternate turns.

In one move, the player must choose a non-empty set $$$s_i$$$ and select an integer $$$x$$$ from the chosen set satisfying $$$x \times p \ge max(s_i)$$$. Then the player should remove all integers not less than $$$x$$$ from this set.

The player who can not make a move loses the game.

You want to know whether the player who goes first will win the game, if both players play optimally.

The first line contains one integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^5$$$) — the number of test cases. The description of test cases follows.

The first line of a test case contains two integers $$$n$$$ and $$$p$$$ ($$$1 \le n \le 2 \cdot 10^5$$$; $$$2 \le p \le 10^9$$$).

Then $$$n$$$ lines follow.

Each of the next $$$n$$$ lines contains two integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \le l_i \le r_i \le 10^ 9$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

For each test case, print a single string in one line. Print "First" (without quotes) if the player makes the first move will win, otherwise print "Second" (without quotes).

4
1 3
1 6
4 100
1 10
2 16
1 7
12 13
3 5
1 8
20 20
13 18
3 2
1 10
2 9
3 4

First
Second
Second
First