CHUNK2 - Popatlal ki shaadi

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Popatlal from Gokuldham Society is still not married.
He approaches a marriage bureau and ask them to hurry the process.
The bureau checks the list of eligible girls (n) and hands it over to Popatlal.
Popatlal being conscious about his marriage, determined to find a girl with maximum connections so that he can gather more information about her.
Accordingly, he looks to figure out the maximum number of girls (from list) who know each other to achieve above purpose.
In order to finalise the girl,he needs to find the Kth prime.
Where k  = largest group of girls who know each other .
Considering Popat's poor knowledge in Maths, he seeks for Jethalal's help for the answer. Now you , being fan of Jethalal, take this prestigious opportunity to solve Popat's marriage issue.
In case no of connections are zero ,print "-1".
Note : Suppose girl "a" knows girl "b" and girl "b" knows girl "c" , then girl "a" also knows girl "c".
Transitivity holds.
Consider 1 composite no.

Popatlal from Gokuldham Society is still not married.

He approaches a marriage bureau and ask them to hurry the process.

The bureau checks the list of eligible girls (n) and hands it over to Popatlal.

Popatlal being conscious about his marriage, determined to find a girl with maximum connections so that he can gather more information about her.

Accordingly, he looks to figure out the maximum number of girls (from list) who know each other to achieve above purpose.

In order to finalise the girl,he needs to find the Kth prime.

Where k  = largest group of girls who know each other .

Considering Popat's poor knowledge in Maths, he seeks for Jethalal's help for the answer. Now you , being fan of Jethalal, take this prestigious opportunity to solve Popat's marriage issue.

In case no of connections are zero ,print "-1".

Note : Suppose girl "a" knows girl "b" and girl "b" knows girl "c" , then girl "a" also knows girl "c".

Transitivity holds.

Consider 1 composite no.


Input:

First line of the input contains t, the number of test cases.

Each line of the test case contains a number n specifying the number of girls and m specifying no of connections.

Each 'm' lines contain u and v denoting that girl u and v know each other.


Output:

Each new line of the output contains Kth prime no .


Constraints:

1<=t<=100

1<=n<=100000

0<=m<=n

1<=u,v<=n


Example:

Input:
1
10 6
1 2
2 3
3 4
4 5
6 7
9 10
Output:
11
Contributed by: Paras Jain

hide comments
chhavi96: 2018-08-30 15:33:10

guys please take care of -1 thing got 3 WA because of that!!!

budds: 2018-08-30 15:17:40

for 7th WA,
check the condition for no connections, print -1;

sdeven_0245: 2018-08-22 18:21:11

those who are saying 7th WA check if your sieve is able to calculate 10^5th prime or not

sdeven_0245: 2018-08-22 18:20:20

simple one

aryan12: 2018-08-20 19:37:42

Its based on disjoint union sets. An easy one!!!

Satyam Mishra: 2018-08-19 20:04:34

WA after 7th. Any idea people ?

aaakash_rai: 2018-08-18 11:25:51

I created a sieve. then found the count of largest group using union find algorithm and printed the prime corresponding to the size of largest group. Still getting WA. Any help?


Added by:chunky_2808
Date:2018-08-02
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Enigma-17-1-Finals