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, CEO and Founder at CodeMask


hide comments
Narendra pal: 2015-05-31 11:53:19

can zero be the value of x or y ??

Naman Goyal: 2015-05-20 21:31:01

Good one, I went in completely wrong direction with prime factorizing a,b and c and wasted quite a lot time.

Bozidar: 2015-04-22 19:04:00

Don't forget to put space betwen ':' and 'Yes' or 'No' . Costed me a hell of nervs....

Dhruv k14: 2015-03-07 20:43:56

and the printing errors cause multiple WAs for the infiniteth time

Indian Cyber Army (IndiShell): 2015-02-03 17:57:46

My 30th :)
Feeling motivated !! :D

Gaurav sharma: 2015-01-30 18:49:20

go green...:P :) before this try ENIGMATH


Added by:Md Abdul 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