Description

Frank and Louis are playing a game with $n$ piles of stones, where the $i$-th pile has $a_i$ stones. Denote the average of sequence $a_1,a_2,\dots,a_n$ as $x$.

Before the game starts, a positive integer not greater than $x$ is given. Frank and Louis take turns making the following moves with Frank going first:

• Choose the $i$-th and the $j$-th piles of stones $(i \neq j)$ satisfying $a_i<x<a_j.$

• Take out $k$ stones from the $j$-th pile and put them into the $i$-th pile of stones.

The player who is unable to make a move loses.

Determine who will win if both players play optimally.

Input Format

Each test contains multiple test cases.

The first line of the input contains a single integer $T$, the number of test cases. The description of test cases follows.

The first line of each test case contains two integers $n$ and $k$.

The second line of each test case contains $n$ integers: $a_1,a_2,\dots,a_n$.

Output Format

For each test case, output F if Frank wins, L if Louis wins, and Draw if the game will never end.

1
5 2
1 5 7 9 13

L

2
6 3
4 7 5 3 1 16
7 2
2 6 4 8 12 4 6

Draw
L

Hint

Example Explanation

In the first example, $a$ is initially $\{1,5,7,9,13\}$, and the average value $x$ of the sequence $a$ is $7$.

One possible game process follows:

1. Frank chooses $i=1,j=5$, and $a$ becomes $\{3,5,7,9,11\}$.

2. Louis chooses $i=1,j=4$, and $a$ becomes $\{5,5,7,7,11\}$.

3. Frank chooses $i=2,j=5$, and $a$ becomes $\{5,7,7,7,9\}$.

4. Louis chooses $i=1,j=5$, and $a$ becomes $\{7,7,7,7,7\}$.

5. Frank is unable to make a move, so Louis wins.

Constraints

Subtasks are used in this problem.

For all tests, it is guaranteed that:

• $1 \le T \le 10$
• $1 \le n \le 2 \times 10^5$
• $0 \le a_i \le 10^9$
• $1 \le k \le x$
• $x$ is an integer.

Special Property A: $a_1=a_2=\dots=a_n$.