Meeting Assistant

Each event has the format person action start end, and the occupied start and end minutes are both inclusive. Within 00:00..23:59, find the earliest k consecutive minutes during which everyone who appears in the events is free. Return −1 if there is no solution; the meeting must not cross into the next day.

输入格式

The first line contains n k, followed by n lines of events; times use the HH:MM format. 1≤n≤100000, 1≤k≤1440, each original event string has length ≤40, the number of people is <5000, and events of the same person do not overlap.

输出格式

Output the earliest time HH:MM, or −1 if it is impossible.

样例 1

输入：

3 60
Alex busy 00:00 08:00
Sam busy 07:00 13:00
Alex busy 12:30 13:59

输出：

14:00

样例 2

输入：

2 1
sam busy 12:00 23:59
alex busy 00:00 13:00

输出：

-1

样例 3

输入：

2 60
sam busy 12:00 18:59
alex busy 00:00 11:00

输出：

19:00

样例说明

The answers to the three public examples are, in order: 14:00; -1; 19:00. The examples were rechecked by independent enumeration, state search, or direct simulation.