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
2015-01-28 19:07:06 M.Srivathsan
finally got AC after 6 submissions
2015-01-27 21:30:54 bharat
sum of long long input can be more than long long....good use of modulo
2015-01-26 20:30:23 Srikant Aggarwal
Well... Took hint from the comments.. Thank you guys!!
2015-01-19 19:52:48 Dushyant Singh
Got AC after 6 submissions! Note: input can be declared using long long int but it is not necessary that sum of all inputs will be long long int. It might be greater than range of long long int. So use % wisely!
Thanks to Davit Safrastyan! :-)

Last edit: 2015-01-23 16:24:12
2015-01-18 14:32:42 Arnabjyoti Kalita
got it ...be careful with the usage of modulo operator... :)
2015-01-18 14:21:50 Arnabjyoti Kalita
Somebody plz say what are the constraints for input...inspite of using unsigned long long for testcases and the other inputs---it is still showing WA...????
P.S. The logic is ok as it works on Ideone

Last edit: 2015-01-18 14:23:05
2015-01-16 14:20:49 harshit sharma
test case prceeded by blank line....what does it means
2015-01-11 01:42:30 Raj Kumar Chauhan
ufff.. evertime i am getting some problem here.
anyone plz help <snip>

Last edit: 2023-06-02 23:43:33
2014-12-26 12:01:17 Shubham Khilari
For C try to use unsigned long long instead og just long long int.Worked for me after 5 WAs!!
2014-12-20 06:08:12 Ankur Singh
big input..
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