Professor Valentin Vladimirovich, member of the Galaxy Academy, tomorrow
takes part in voting for nomination “The Best Picture”. But professor haven’t
watched any of n nominee movies yet and he doesn’t in fact have time today. He
decided to ask help from his k students, who still haven’t got credit for
his subjects. If the students watch all the movies and then tell professor briefly
about their impressions, this information will be enough to make a
choice.
Each of the nominee movies is shown in the movie halls only once, the i'th movie
starts at time a_{i} and finishes at time b_{i}. A student can watch any
number of movies through the day, but he must watch each one from start
to finish. A student can’t watch two movies simultaneously. It is also
known that c_{i} beautiful actresses star in the i'th movie. A student won’t go
for a movie if less actresses star in it than in the previous movie he
watched.
Valentin Vladimirovich gave students detailed instructions in case
they can’t watch all the movies in one day. The movies are numbered in descending
order according to descending popularity of their directors. If students
can see either set
A of movies or set
B of movies, the set
A is more preferable
if there is such
i that:
 the movies with numbers from 1 to i − 1 are either present in both sets
A and B, or not present in neither A nor B;
 the i'th movie is present in the set A and is not present in the set B.
Find the most preferable set of movies for Valentin Vladimirovich and his students.
Input
The first line contains integers n and k (1 ≤ n ≤ 100;
1 ≤ k ≤ n). The ith of the next n lines contains integers
a_{i}, b_{i}, c_{i} (0 ≤ a_{i} < b_{i} ≤ 86 399; 1 ≤ c_{i} ≤ 10 000).
Output
Output a string of n digits, specifying the most preferable set of movies.
One should be at the position i if the i'th movie is present in this set, and
zero should be there in the opposite case.
Samples
input  output 

4 2
1 5 10
3 6 20
5 10 9
5 10 10
 1101

4 1
1 5 10
3 6 20
5 10 9
5 10 10
 1001

Problem Author: Vitaliy Belokobilskiy, Sergey Madzhuga
Problem Source: Open Ural FU Personal Contest 2012