Pusheen has been dreaming about tuna sashimi! She has decided that she needs to eat more tuna in her life, so she decides to visit ~T~ restaurants to eat tuna sashimi and tuna nigiri.
Each restaurant that Pusheen wishes to visit sells sashimi and nigiri at their own prices - restaurant ~i~ sets their prices at ~A_i~ dollars per piece of tuna sashimi and ~B_i~ dollars per piece of tuna nigiri. Pusheen has decided that before tax and tip, the amount of money she spends should be exactly ~N_i~ dollars for restaurant ~i~. Is it possible for Pusheen to spend exactly ~N_i~ dollars on sashimi and nigiri? (Don't worry, she's budgeted money for the tip!)
~1 \le T \le 2500~
~1 \le A_i \le B_i \le 50~
~1 \le N_i \le 50~
In tests worth 3 marks, ~A_i = 1~.
In tests worth an additional 3 marks, ~B_i~ will be divisible by ~A_i~.
The first line contains a single positive integer ~T~, the number of times Pusheen repeats this exercise.
Each of the next ~T~ lines contains three positive space-separated integers, ~A_i~, ~B_i~, and ~N_i~, indicating that her favourite sushi restaurant is charging ~A_i~ dollars per piece for sashimi and ~B_i~ dollars per piece for nigiri, and Pusheen's budget purely for the sashimi and nigiri is ~N_i~ dollars.
Output ~T~ lines. If Pusheen can order items accordingly from the ~i~th restaurant, output
YES on the ~i~th line.
2 2 2 2 3 4 5
In the first example, Pusheen can order either one piece of sashimi or one piece of nigiri.
In the second example, Pusheen is unable to order exactly 5 dollars of items from sashimi or nigiri. One piece of nigiri costs four dollars, but two pieces of sashimi cost six dollars.