CEQU  Crucial Equation
Let us see the following equation,
ax+by=c
Given three positive integers a, b and c. You have to determine whether there exists at least one solution for some integers value of x and y where x, y may be negative or nonnegative integers.
For example if a=2, b=4 and c=8 then the equation will be 2x+4y=8, and hence, for x=2 and y=1, there exists a solution.
Let us see another example for a=3, b=6 and c=7, so the equation will become 3x+6y=7 and there exists no solution satisfying this equation.
Input
Input starts with an integer T (1<=T<=10^{5}) denoting the number of test cases. Each test case contains three integers a, b, and c. (1<=a, b, c<=10^{6}).
Output
For each test case of input print the case number and “Yes” if there exists at least one solution, print “No” otherwise.
Sample Input 
Output for Sample Input 
2 
Case 1: Yes 
Problem Setter: Md Abdul Alim, Dept. of Computer Science, Bangladesh University of Business & Technology
hide comments
pennywise_123:
20230119 14:10:52
Be Careful with output form Last edit: 20230119 14:11:33 

dawnwillcome:
20220709 03:48:51
Bézout's Lemma 

trunghieu06:
20220704 09:04:20
I submitted 4 times because the output format xD 

ayu_031201:
20220110 07:19:02
output format is this >


rithwhick_2003:
20211023 16:07:13
got it if u didnt get it dont feel low..try your best and learn linear diaphantine eqution


rithwhick_2003:
20211023 16:04:36
some one help..at a very brute force i could think of..let c2=b%a,c1=c%a....and i would run a loop of i=0 to a1;


rimuru_404:
20211011 13:03:57
Formatting the output was tougher than the actual problem _ 

itsabi_z1:
20210622 06:05:01
pay attention to the output format. 

anchord:
20210607 06:30:31
Good question! only about the basic concept about linear diophantine, pretty simple 

crawler_123:
20210423 20:01:27
The Problem is based on finding solution for Linear Diophantine Equation, hope this hint will help any one of you. 
Added by:  Alim 
Date:  20141015 
Time limit:  3s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 GOSU 
Resource:  Own Problem 