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
hide comments
akshayvenkat:
20160612 10:05:17
little corner case modification to CEQU and AC! 

lakshay_v06:
20160125 08:50:28
Prerequisites : Diophantine equation and Extended euclids algo. :) 

thedictator:
20151210 13:49:35
too easy if the logic strikes in your mind 

bunnycoder:
20151020 17:16:44
AC in one go had to think a lot about the logic 

rahul_verma:
20150926 19:55:41
same as CEQU just copy the code and change output format got AC!!! 

Kaustubh Mallik:
20150926 15:09:59
@hello_word @Kushal Saharan: Read the question carefully. It says you should have "z" litres of water in one of the jugs at the end, from where Manku has to drimk. The second last statement of the problem has it. "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." You should read the problem statements carefully rather than blaming the judge or saying the incorrectly framed question. 

geoffreymace7:
20150816 15:28:45
:) 

rrv:
20150716 19:27:57
remember you have to drink only once from any one of the jugs n any one of them must be able to hold z litres of water 

mrx:
20150706 16:20:43
lol, no special logic required :P 

aparna00:
20150609 20:13:11
does it mean dat manku can drink from only one of the two glasses ? otherwise ans for 6 4 10 wud have been a YES !! 
Added by:  Mayank Tuteja 
Date:  20130117 
Time limit:  0.187s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
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