Stone Game

Roland P. Sprague and Patrick M. Grundy were both enthusiasts of combinatorial games, but they had never met.

One day, in a letter to Grundy, Sprague introduced an ancient game allegedly from the East—the Stone Game.

The Stone Game is a two-player game. At the beginning of the game, there are several piles of stones on the table. The two players take turns: a player chooses a pile and removes any number of stones from it (but must remove at least one). The player who cannot make a move loses, and the other player wins.

Due to limited conditions, Sprague suggested writing a row of natural numbers on a piece of paper to represent the number of stones in each pile, and then the two players would take turns crossing out numbers and writing new ones. Grundy gladly agreed.

A month later, after Grundy had lost five games in a row, he suspected Sprague of cheating. After a few days of research, Grundy discovered one afternoon that if both players are sufficiently intelligent, there is a very simple way to determine whether the first player or the second player will win, given an initial state (a row of natural numbers), and one can even provide a winning strategy! Thus, Grundy decided to strike back.

The next day, in a letter to Sprague, Grundy suggested making the game rules more complex: first, determine a constant $K$. Then, the rules for both players change: each turn, a player chooses a number to cross out. Suppose the number is $x$. The player can choose a positive integer $a$, and after crossing out $x$, they must write down $K$ numbers: $x - a, x - 2a, \dots, x - Ka$, provided that $x - Ka \ge 0$. If no such $a$ exists, the player cannot cross out this number $x$. The condition for losing remains the same: the player who cannot make a move loses.

Out of pride, Sprague could not refuse. However, he would not sit idly by. Now he has obtained $K$ and the $N$ numbers written on the paper. He has told you—John von Neumann—all this data and the rules of the game, as you are a mathematician, physicist, economist (and computer scientist) studying how to use a machine that does not yet exist (which you have named a computer) to solve practical problems.

Input

The first line contains a positive integer $T$, representing the number of test cases (the number of times Sprague asks you). Then $T$ test cases follow. Each test case occupies $N + 2$ lines, formatted as follows:

The first line is an empty line. The second line contains two positive integers, $N$ and $K$, in that order. The next $N$ lines each contain a positive integer, representing the $N$ numbers written on the paper.

Output

The output contains $T$ lines. For each test case, if the first player has a winning strategy, output "Preempt.". If the second player has a winning strategy, output "Leapfrog.". If neither is the case, output "Je suis un imbecile.".

Examples

Input 1

2

1 1
1

2 30
197943
249832

Output 1

Preempt.
Leapfrog.

Constraints

• 10% of the data: $N \le 5, K = 1$, all numbers $\le 5$.
• 20% of the data: $N \le 100, K = 1$, all numbers $\le 10^9$.
• 10% of the data: $N \le 100, K = 2$, all numbers $\le 10^9$.
• 20% of the data: $N \le 100, K = 2$, all numbers $\le 10^{18}$.
• 20% of the data: $N \le 100, K = 10$, all numbers $\le 10^{18}$.
• 40% of the data: $N \le 100, K = 30$, all numbers $\le 10^{80}$.
• 100% of the data: $T \le 10$.