CANDY3 - Candy III

A class went to a school trip. And, as usually, all N kids have got their backpacks stuffed with candy. But soon quarrels started all over the place, as some of the kids had more candies than others. Soon, the teacher realized that he has to step in: "Everybody, listen! Put all the candies you have on this table here!"

Soon, there was quite a large heap of candies on the teacher's table. "Now, I will divide the candies into N equal heaps and everyone will get one of them." announced the teacher.

"Wait, is this really possible?" wondered some of the smarter kids.

Problem specification

You are given the number of candies each child brought. Find out whether the teacher can divide the candies into N exactly equal heaps. (For the purpose of this task, all candies are of the same type.)

Input specification

The first line of the input file contains an integer T specifying the number of test cases. Each test case is preceded by a blank line.

Each test case looks as follows: The first line contains N : the number of children. Each of the next N lines contains the number of candies one child brought.

Output specification

For each of the test cases output a single line with a single word "YES" if the candies can be distributed equally, or "NO" otherwise.

Example

Input:
2

5
5
2
7
3
8

6
7
11
2
7
3
4

Output:
YES
NO
Note: the input file will not exceed 1MB.

Added by:Fudan University Problem Setters
Date:2007-12-01
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: C99 ERL JS-RHINO
Resource:IPSC 2006

hide comments
2017-08-16 10:48:28
felt happy!!
truly a tricky one!!thnx @softxide
2017-08-12 09:00:39
I believe that not specifying input range is the core catch of this problem - the problem wants us to use modulo arithmetic while summing - instead of calculating sum (which can extend datatype limits -do modulo inplace )
2017-08-07 18:34:11
input range should be given!
Use long long
2017-08-07 12:01:03
Solvable using int if you know your modulo arithmetics
2017-07-26 04:28:23
total stupidity....range should have been mentioned in the problem
2017-07-22 13:20:31
At first use int and get WA
Finally use long long and get AC :)
It's a good problem for beginners.
2017-07-13 16:49:09
nice question...but be careful for large inputs.
2017-06-26 17:16:48
Without modulo i was getting wrong answer but when i solved it using modulo my solution got accepted but I still wonder what the error was without modulo .I am new to programming .Can somebody just help me out?
2017-06-26 16:37:34
limits should be mentioned.
2017-06-14 10:49:46
@monster_666
just add extra input() in your code after test cases loop
#create loop for test cases
#input() <---- add this it will accept blank spaces
#YOUR CODE
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