Air Conditioner

Time limit1sMemory limit1024 MB

Summary

Given day N and a clock delay of K minutes, list every time the air conditioner switches off on day N, where each third shutoff stops the internal clock for K minutes.

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

Problem

Most DGIST undergraduate students live in the dormitory. As summer approaches, they will use a cool air conditioner whose temperature can be set freely. Unfortunately, the air conditioner is designed to switch off automatically every day at exactly 15:00, 18:00, and 21:00. Also, its internal clock is broken, so every time it switches off for the third time, the clock stops for $K$ minutes.

Jung Digi wanted a machine that turns the air conditioner back on exactly on the hour, so she can take a comfortable nap. She became angry when the air conditioner did not turn on at the right time. Before she assigns a circuit theory project, you need to build a machine that predicts the time the air conditioner switches off on day $N$ and turns it on again, so that Jung Digi stops being angry. (Days start at 00:00 on day 0, and the air conditioner is on at the start.)

Input

Two integers are given on one line, separated by a space: $N$ , the day number, and $K$ , the number of minutes of delay. $(0 \le N \le 1,000, 0 \le K < 60)$

Output

On the first line, print $M$ , the number of times the air conditioner switches off on day $N$ .

On the following $M$ lines, print the times the air conditioner switches off in ascending order, in the form $hh:mm$ .

Examples2

Example 1
Input
```
0 0
```
Expected output
```
3
15:00
18:00
21:00
```
Example 2
Input
```
1000 59
```
Expected output
```
3
02:00
05:00
23:59
```