Problem: A Darie is a special circle. Numbers 1, 2, ..., n are written clockwise around this circle in order. You can stand on a number! Initially Rasta is on number 1. In each step, he jumps exactly p numbers clockwise. For example if n = 3 and he is standing on number 1:

If p = 1 then he jumps to number 2.

Or if p = 2 he jumps to number 3.

He does this until he reaches a number he's been on before (for example, if n = 3, p = 1 he stops after three jumps).

Then he writes down the numbers he had been on, as a sequence s in increasing order.

He's not a Mr.Memmory, so he can't remember this sequence. He asks you to help him by telling him the k-th number in this sequence (or -1 if size of s is less than k).

Input format
The first line of input contains an integer t, the number of testcases (1 ≤ t ≤ 10^5).

Each testcase is given in one line, which contains three integers n, p, k (2 ≤ n ≤ 10^6, 1 ≤ p ≤ n - 1, 1 ≤ k ≤ 10^6).

Output format
Print the answer of each testcase in one line.

SAMPLE INPUT
3
12 5 3
12 3 2
3 2 2

SAMPLE OUTPUT
3
4
2

Solution (in PYTHON):

Solution:
def gcd(a,b):
    if b==0:
        return a
    else:
        return gcd(b,a%b)

t=int(input())

while t>0:
    n,p,k=raw_input().split(' ')
    a=[1,1]
    n=int(n)
    p=int(p)
    k=int(k)
    if gcd(n,p)==1:
        if k>n:
            res=-1
        else:
            res=k
    else:
        temp=gcd(n,p)
        if k>(n/temp):
            res=-1
        else:
            res=(temp*(k-1))+1
    print res
    t=t-1