Credibility of Witnesses

Memory limit: 32 MB

Witnesses, numbered from to , have made their testimonies in a court. Each testimony is a statement of the form: “the -th witness agrees with the -th witness” or “the -th witness does not agree with the -th witness”.

If the -th witness agrees with the -th witness then he agrees also with all the witnesses that the -th witness agrees with. Similarly, the -th witness does not agree with all the witnesses that the -th witness does not agree with. We assume that every witness implicitly states: “I agree with myself”.

We say that witness is not credible if from testimonies made in a court it follows that there exists a witness such that agrees with and does not agree with .

Task

Write a program that:

• reads the number of witness and their testimonies from the standard input,
• finds all the witnesses that are not credible,
• writes the result to the standard output.

Input

In the first line of the standard input there is a single integer , , which is the number of witnesses. In the second line there is a single integer , , which is the number of testimonies.

In each of the following lines there are two integers (, ), separated by a single space. If is positive it describes a testimony: “the -th witness agrees with the -th witness”. If is negative it means: “the -th witness does not agree with the -th witness”.

Output

In the standard output there should be written:

• a single word NIKT (which means “nobody” in Polish), if it follows from testimonies that there is no witness that is not credible,
• or — in increasing order — the numbers of witnesses that are not credible (one member in one line).

Example

For the input data:

6
12
1 3
1 6
2 -1
3 4
4 1
4 -2
4 5
5 -1
5 -3
5 2
6 5
6 4

the correct result is:

1
3
4
6

Task author: Grzegorz Jakacki.