The 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, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the 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.

×
E. Help Shrek and Donkey

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputShrek and the Donkey (as you can guess, they also live in the far away kingdom) decided to play a card game called YAGame. The rules are very simple: initially Shrek holds *m* cards and the Donkey holds *n* cards (the players do not see each other's cards), and one more card lies on the table face down so that both players cannot see it as well. Thus, at the beginning of the game there are overall *m* + *n* + 1 cards. Besides, the players know which cards the pack of cards consists of and their own cards (but they do not know which card lies on the table and which ones the other player has). The players move in turn and Shrek starts. During a move a player can:

- Try to guess which card is lying on the table. If he guesses correctly, the game ends and he wins. If his guess is wrong, the game also ends but this time the other player wins.
- Name any card from the pack. If the other player has such card, he must show it and put it aside (so that this card is no longer used in the game). If the other player doesn't have such card, he says about that.

Help Shrek assuming the pills are good in quality and that both players using them start playing in the optimal manner.

Input

The first line contains space-separated integers *m* and *n* (0 ≤ *m*, *n* ≤ 1000).

Output

Print space-separated probabilities that Shrek wins and Donkey wins correspondingly; the absolute error should not exceed 10^{ - 9}.

Examples

Input

0 3

Output

0.25 0.75

Input

1 0

Output

1 0

Input

1 1

Output

0.5 0.5

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/10/2022 16:40:15 (g2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|