401825: GYM100534 H Dreams Were Important Too!

Memory Limit:256 MB Time Limit:3 S
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Description

H. Dreams Were Important Too!time limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

A few years ago, some silly guys stole a keyboard and an antiquated flag from a site. What do you think about the reaction of the administrator? It's obvious, he used all he could to return the flag and the keyboard. Whole country were searching for an entire month and many hypotheses had been proposed by funny people.

After a few years, another robbery happened. This time it was very complex, organized and supported by a big country. The robbers started their plan many years ago when we were limiting and rationing our site's capacity. Finally robbers succeeded to stole a "dream" from the site! This time the admin was surprised. After exchanging a few ineffective emails the poor stolen dream was forgotten and the admin said: "Instead of off topic discussions just suggest how you can help us for next year! We are too busy!" and real reasons were easily forgotten. "Finally the stolen dream remained just a dream!"

Let's get back to the story of the stolen flag. You should try to convince an unknown person that recreating a stolen triangular flag is not a hard task. You are given area and perimeter of the flag and you have to find integer coordinates of its vertices.

Input

The single line contains two positive space-separated integers A2 and P (1 ≤ A2 ≤ 4 × 104, 1 ≤ P ≤ 104). A2 is twice the area and P is perimeter of the flag.

Output

If it's impossible to recreate the flag, output in the single line "Flag" (without quotes) Otherwise output in the first line "Dream" (without quotes). In the next three lines output the coordinates of the triangle vertices. Each line should contain two space separated integers, each in range [ - 106, 106].

ExamplesInput
12 12
Output
Dream
-1 2
2 6
2 2
Input
15 15
Output
Flag

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