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
2015-07-15 19:59:59 Akshay Aradhya
Would have solved this problem if the constraints were given. Use long int people.
2015-07-04 09:53:01
YOU CAN FIND THE SOLUTION IN C++ HERE
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Last edit: 2023-06-02 23:41:19
2015-06-10 09:13:51 Ankush
Please remove the extra spaces in input. Costed me 2 RE NZEC in Python.
2015-06-09 21:27:36 tin-tin
Comments saved the day, thanks!
AC in one go...
2015-06-02 21:01:29 Pinaki Dash
Please help me with my code. Iam getting wrong answer here but is working perfectly for all test cases
<snip>

Last edit: 2023-06-02 23:41:25
2015-06-01 14:32:27
how to obtain new line in between them .should we print or scan space there
2015-05-29 06:46:26 studmax
Comments Helped.., Careful about how you apply modulo operator "sum of long long int's may be larger than long long int" ===> This sentence helped me (adapted from comments). Thank You

Last edit: 2015-05-29 06:46:53
2015-05-25 16:19:05 Amit
I am using long long int and sum = ((sum%n)+(numcandy%n))%n but it's showing time limit exceeded..... Can anybody help me in reducing the time complexity of the problem....
2015-05-25 11:20:28
Got AC after 3 WA.......Calculate sum wisely....Keep sum as low as possible
Hint:when n=5...val 6 and val 1 have the same impact on sum
2015-05-21 19:09:32 Adarsh K
Bad question. Must mention the limit in question
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