ADAGCD - Ada and GCD


Ada the Ladybug got interesting homework. She had to count gcd of a few numbers. As she is a great mathematician, she done it in meanwhile (in fact, she submited it during the class it was assigned in). The teacher was impressed so he gave Ada a bonus homework (for bonus points). It is same as previous one with a little difference - there are bigger numbers.

Since the number are too large to be written as numbers, they are written as product of lesser numbers. Find their gcd.

Input

The first line of input consists of 2 ≤ N ≤ 106, the number of numbers for which Ada wants to find their gcd.

Each of the next N lines contains an integer 1 ≤ Mi < 106 followed by Mi integers, 1 ≤ Aj ≤ 107, the numbers whose product is the ith number.

The sum of all Mi won't exceed 106

Output

Print the gcd on a single line. Since this number might be pretty big, output it modulo 109+7 (1000000007)

Example Input 1

3
4 1 2 3 4
1 36
2 6 5

Example Output 1

6

Example Input 2

2
11 1 2 3 4 5 6 7 8 9 10 11
2 1024 15 

Example Output 2

3840

hide comments
kumar_07: 2021-06-14 18:25:41

Please help!!
It's giving me a runtime error on 15th TC.
can anybody help me with this issue???

the_art_maniac: 2021-06-04 11:21:46

great question for gcd , keep in mind the big numbers! :)

ratkill: 2021-05-21 16:39:51

@morass : cannot make it work , no matter what i do. The logic seems fine for regular numbers but it doesn't seem to work for big numbers.

wille_25: 2021-01-09 16:40:24

Finally did it (took 7.13s)
take modulo everywhere you multiply

yaseenmollik: 2020-06-12 06:11:34

It took 7 runtime error to solve this problem finally!

nitishyadav169: 2018-11-22 20:59:15

Help!
On 15 TC it gives NZEC .
I Code in java.
Any Type of Suggestion will be Appreciated.

hodobox: 2017-07-27 22:19:01

easier version is http://www.spoj.com/problems/HG/
:)

Last edit: 2017-07-27 22:19:15
shubham: 2017-06-09 11:05:59

AC in one go.. :)

shubham: 2017-06-09 11:05:37

AC in one go.. :)

pvsmpraveen: 2017-04-14 13:08:17

@morass : can you check my solution? *_*

Found the bug myself!
The irony is, i found the bug in my template which gave wrong for large numbers which i cannot find before,while solving another problem today i found that bug and revisited this problem after 1 month to get an AC :)

Last edit: 2017-04-25 16:36:04

Added by:Morass
Date:2017-02-11
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All