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THREENUMBERS - nth number

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Given two numbers a and b, you have to find n-th number which is divisible by a or b.

Input

First line contains an integer T (≤ 100000), denoting number of test cases.

Second line contains 3 positive integers a, b and n. (a, b ≤ 10000, n ≤ 1000000000)

Output

Print n-th number in a new line.

Example

Input:
1
2 3 10

Output:
15

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	Aleksandar Kostadinov: 2017-09-11 21:46:55 @wisfaq: Thanks for usefull hint!
	wisfaq: 2017-09-11 20:44:38 @David (and others having problems with NZEC) One of the ways to overcome those problems is to use error handling. Something like: try: __read a,b,n __get answer(a,b,n) __store answer __print answer except: _print stored (previous) answer. That's the way I got AC with Python Last edit: 2017-09-11 20:48:39
	David N. Springer: 2017-09-11 15:30:37 If I check for premature EOF, I get WA otherwise I get NZEC. Please help. How to handle missing testcase?
	vengatesh15: 2017-09-11 08:27:26 easy one ..
	kkgujjar: 2017-09-10 20:01:59 can anyone send me the hint or solution of this problem ??
	asdadqwerty: 2017-09-09 21:50:31 No editorials on SPOJ? =(Francky)=> We keep an eye. Always. Last edit: 2017-09-10 08:25:01
	asdadqwerty: 2017-09-09 21:50:01 Can someone please help me with the logic? I tried using binary search. didnt work
	testing java: 2017-09-09 17:04:14 Input is wrong. I changed my program to version in which: if there is no new value in the input stream, i keep old value in variables a,b,n. Got AC.
	shubham_001: 2017-09-09 16:31:32 Test cases are correct! but this problem is copied directly :\| ,plz make something by atleast some modifications :)
	testing java: 2017-09-09 15:57:41 My guess is that the actual number of tests is smaller than given t. If my reader does not blow up in such case, I have WA (as I'm printing nothing or some rubbish), otherwise i have NZEC. It may be the case that my program is faulty (hence WA), however I think, that there may be something wrong with the input (as change in handling cases which should not happen, change status of my submission).

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Added by:	surayans tiwari
Date:	2017-09-09
Time limit:	1s
Source limit:	50000B
Memory limit:	1536MB
Cluster:	Cube (Intel G860)
Languages:	All
Resource:	SELF