MAKETREE - Hierarchy

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A group of graduated students decided to establish a company; however, they don't agree on who is going to be who's boss.

Generally, one of the students will be the main boss, and each of the other students will have exactly one boss (and that boss, if he is not the main boss, will have a boss of his own too). Every boss will have a strictly greater salary than all of his subordinates - therefore, there are no cycles. Therefore, the hierarchy of the company can be represented as a rooted tree.

In order to agree on who is going to be who's boss, they've chosen K most successful students, and each of them has given a statement: I want to be the superior of him, him, and him (they could be successful or unsuccessful). And what does it mean to be a superior? It means to be the boss, or to be one of the boss' superiors (therefore, a superior of a student is not necessary his direct boss).

Help this immature company and create a hierarchy that will satisfy all of the successful students' wishes. A solution, not necessary unique, will exist in all of the test data.

Input

In the first line of input, read positive integers N (N ≤ 100 000), total number of students, and K (K < N), the number of successful students. All students are numbered 1..N, while the successful ones are numbered 1..K.

Then follow K lines. In Ath of these lines, first read an integer W (the number of wishes of the student A, 1 ≤ W ≤ 10), and then W integers from the range [1, N] which denote students which student A wants to be superior to.

Output

Output N integers. The Ath of these integers should be 0 if student A is the main boss, and else it should represent the boss of the student A.

Example

Input:
4 2
1 3
2 3 4
Output:
2
0
1
2
Input:
7 4
2 2 3
1 6
1 7
2 1 2
Output:
4
1
1
0
4
2
3

hide comments
Gaurav Dahima: 2016-10-07 10:16:49

Surprisingly AC in 2nd go (First one was TLE due to cin).
note: there will be always one main boss. :)

hodobox: 2016-09-03 07:59:32

O(nlogn) requires constant optimization :/

kartikay singh: 2016-07-01 10:09:20

Topological sorting :-)

Projjal Kundu: 2015-12-15 12:55:36

Is it a binary tree? or we can assume any general tree

sahni: 2015-01-17 12:25:47

100th one :):P

Aditya Joshi: 2014-11-24 15:49:27

Increase the time limit. Not a single solution in Java. I am getting TLE even though my approach complexity is what is expected.

DP: 2014-07-22 03:54:36

Was getting TLE, changed cin to scanf and cout to printf. Got AC.

parbays: 2014-01-22 19:14:16

Phew...wasted my time, where mistakenly a cout n times was causing TLE.

Bharat Jain: 2013-07-20 18:36:47

any more test case ??

Pranay: 2012-10-29 05:58:32

@Adrian : Could you please tell why WA (id: 7953672) ? Also Can't there be 2 main bosses ? E.g for case 1 , can't the answer be 0 0 2 2 ?

Last edit: 2012-10-29 07:01:37

Added by:Adrian Satja Kurdija
Date:2011-04-15
Time limit:0.119s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:own problem