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The Public Peace Commission should be legislated in Parliament of The Democratic Republic of Byteland according to The Very Important Law. Unfortunately one of the obstacles is the fact that some deputies do not get on with some others.
The Commission has to fulfill the following conditions:
Write a program, which:
In the first line of the standard input there are two non-negative integers and . They denote respectively: the number of parties, , and the number of pairs of deputies, who do not like each other, . In each of the following lines there is written one pair of integers and , , separated by a single space. It means that the deputies and do not like each other.
The standard output should contain one word NIE (means NO in Polish), if the setting up of the Commission is impossible. In case when setting up of the Commission is possible the standard output should contain integers from the interval from to , written in the ascending order, indicating numbers of deputies who can form the Commission. Each of these numbers should be written in a separate line. If the Commission can be formed in various ways, your program may write any of them.
For the input data:
3 2 1 3 2 4
the correct result is:
1 4 5
Task author: Wojciech Rytter.