405709: GYM102052 A The Game

Intellectual TV-game "What? Where? When?" is very popular. Throughout the game, a team of experts attempts to answer questions sent in by viewers. If experts answer the question correctly, one point is awarded to the team of experts, otherwise a point is awarded to the team of viewers. The game ends when one of the teams scores $$$k$$$ points.

You are given a final score of $$$x:y$$$. So the game consisted of $$$x + y$$$ questions asked, and one of the teams scored exactly $$$k$$$ points. You are not given $$$k$$$, since you can calculate it easily. You are asked to find any valid game scenario that finished with score $$$x:y$$$, as the list of scores after each question asked.

The score you are given is correct, and at least one question was asked.

The first line consists of two integers $$$x$$$ and $$$y$$$, the final score ($$$0 \le x, y \le 1000$$$; $$$x \ne y$$$).

Print $$$x + y$$$ lines, $$$i$$$-th of them containing a score after $$$i$$$-th round. The numbers of points scored have to be separated by colon character (':'). You can print any game scenario that finishes with score $$$x:y$$$.

Testing data for this problem consists of 10 test cases. For solving each test case you are awarded 10 points. Total score is the total sum of points for all test cases. The testing verdict for each test case is shown.

3 4

1:0
2:0
2:1
2:2
3:2
3:3
3:4

5 1

1:0
2:0
3:0
4:0
4:1
5:1