The Game

Time limit1sMemory limit512 MB

Summary

Given a final score x:y where one team reached k points, reconstruct any valid sequence of scores after each question.

Level: Easy3 of 10
Topics: Greedy, Implementation, Simulation
Solved: No attempts yet

Problem

The intellectual TV game "What? Where? When?" is very popular. Throughout the game, a team of experts tries to answer questions sent in by viewers. If the experts answer a question correctly, the team of experts gets one point; otherwise, the team of viewers gets one point. The game ends when one of the teams reaches $k$ points.

You are given a final score of $x:y$ . The game therefore consisted of $x + y$ questions, and one of the teams scored exactly $k$ points. You are not given $k$ , since you can compute it easily. Find any valid game scenario that ended with the score $x:y$ , as the list of scores after each question.

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

Input

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

Output

Print $x + y$ lines. The $i$ -th line contains the score after the $i$ -th round. Separate the two point totals with the colon character (':'). You may print any game scenario that ends with the score $x:y$ .

Examples2

Example 1
Input
```
3 4
```
Expected output
```
1:0
2:0
2:1
2:2
3:2
3:3
3:4
```
Example 2
Input
```
5 1
```
Expected output
```
1:0
2:0
3:0
4:0
4:1
5:1
```