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 non-negative 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<=105) denoting the number of test cases. Each test case contains three integers a, b, and c. (1<=a, b, c<=106).

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
2 4 8
3 6 7

Case 1: Yes
Case 2: No

Problem Setter: Md Abdul Alim, Dept. of Computer Science, Bangladesh University of Business & Technology


hide comments
pennywise_123: 2023-01-19 14:10:52

Be Careful with output form

Last edit: 2023-01-19 14:11:33
dawnwillcome: 2022-07-09 03:48:51

B├ęzout's Lemma

trunghieu06: 2022-07-04 09:04:20

I submitted 4 times because the output format xD

ayu_031201: 2022-01-10 07:19:02

output format is this ->
cout<<"Case "<<i<<": Yes"<<endl;
cout<<"Case "<<i<<": No"<<endl;
just copy paste it for better understanding :)

rithwhick_2003: 2021-10-23 16:07:13

got it if u didnt get it dont feel low..try your best and learn linear diaphantine eqution

rithwhick_2003: 2021-10-23 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 a-1;
so that (c2*i)%a ==c1 and c2*i<=c1 ...i could only think of this..and obviously constraints breaks at certain time due to 1e6 of a ....so i need a better optimization or any other method to solve this

rimuru_404: 2021-10-11 13:03:57

Formatting the output was tougher than the actual problem -_-

itsabi_z1: 2021-06-22 06:05:01

pay attention to the output format.

anchord: 2021-06-07 06:30:31

Good question! only about the basic concept about linear diophantine, pretty simple

crawler_123: 2021-04-23 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:2014-10-15
Time limit:3s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU
Resource:Own Problem