MAY99_3  Easy Jug
One day Manku was very thirsty , so he decided to drink exactly z litres of water .
However , in front of him, there is a well of infinite amount of water and 2 empty jugs of quantity x litres and y litres respectively.
Now Manku can do the following operations to any jug
1> Fill it completely from the well
2> Empty it entirely
3> Transfer as much water from Jug 1 to Jug 2 , till Jug 1 gets empty or Jug 2 is completely filled.
Now since he has no measuring device so he will do these operations only to make any of the 2 jug having exactly z litres of water.
Now Your task is given value of x,y,z , tell whether it is possible for Manku to drink water or not.
Input
First Line of Input contains t , no. of test cases. (t<=25)
Then for each test case there are 3 no's x,y,z given in separate line
1<=x<=10^8
1<=y<=10^8
1<=z<=10^8
Output
For each test case output "YES" if manku can drink exactly z litres of water else "NO".
Example
Input: 5
2 4 3
2 5 1
9 3 6
3 8 7
6 1 10
Output: NO
YES
YES
YES
NOExplanation
In Test case 1 Either Manku can have 2 or 4 litres of water so he cant drink 3 litres
In Test case 2 Manku can have 1 litre water by doing the following operations
> Fill 2 litre Jug
> Transfer its water to 5 litre Jug
> Again Fill 2 litre Jug
> Again Transfer its entire water to 5 litre Jug
Now 5 litre Jug will have total 4 litre water>Again Fill 2 litre Jug
> Now transfer 1 litre water to 5 litre Jug
because at present 5 litre Jug don't have space for more than 1 litre water
Now the 2 litre Jug will have only 1 litre water leftFor Test case 3 we will transfer 3 litre water twice from 3 litre jug to 9 litre jug
For test Case 4 , transfer 3 times water of 3 litre jug to 8 litre jug
Ultimately 3 litre Jug has 1 litre water left and 8 litre Jug is full
Now empty 8 litre jug and pour remaining 1 litre of 3 litre jug in it
Now fill 3 litre jug fully twice and transfer its water to 8 litre jugNow 8 litre Jug will have 7 litre water
For Test case 5, we cant have 10 litre of water in any jug
Added by:  Mayank Tuteja 
Date:  20130117 
Time limit:  0.187s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel Pentium G860 3GHz) 
Languages:  ASMGCC C C++ 4.3.2 C++ 4.9 C++14 COB GROOVY JAVA JS2 PYPY PY3.4 VB.net 
hide comments
__hk__:
20150527 11:47:44
Nice Problem...I changed my logic entirely after getting 1 WA... :) 

Itachi_Uchiha:
20150220 14:58:49
plz provide more test cases


Kushal Saharan:
20140621 04:20:10
Incorrectly framed question. People take care.


Mitch Schwartz:
20140213 17:56:59
@hello_world: (This applies to problems in general.) Let S = set of all possible inputs; C = set of inputs that your code gives correct answers for; W = S \ C; I = set of inputs in the actual test data. Now consider when W is nonempty and (I intersect W) is empty. You should know that incorrect test data is not the same as weak test data, and also consider the degree of weakness. Of course for some problems letting I = S is infeasible. Last edit: 20140213 17:59:46 

hello_world:
20140213 16:58:03
@mitch so doesn't that mean it rejects the "actually" correct answer, in other cases also?...because the code is same..may result in WA for a genuine code 

Mitch Schwartz:
20140213 15:47:21
@hello_world: Incorrect code getting AC does not imply the test data or judge is incorrect. Correct code getting WA would imply that. 

hello_world:
20140213 15:14:21
Accepted solution gives wrong answer for case


RAMSDEN:
20140126 18:29:54
easy to crack 

Anubhav Balodhi :
20140122 07:12:50
This problem (Die Hard Water jug puzzle) is giving countless no. of Wa just because of a slight variation... 

Aayush Moroney:
20131226 18:53:02
4 WA just bcz of my never ending silly mistakes...finally AC ;) 