There is a n×m network. You are remaining at cell (1,1) and your objective is to complete at cell (n,m).    You can move to the adjoining cells to one side or down. All in all, assume you are remaining at cell (x,y). You can:    move right to the cell (x,y+1) — it costs x burles;

Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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There is a n×m network. You are remaining at cell (1,1) and your objective is to complete at cell (n,m). 

 

You can move to the adjoining cells to one side or down. All in all, assume you are remaining at cell (x,y). You can: 

 

move right to the cell (x,y+1) — it costs x burles; 

 

drop down to the cell (x+1,y) — it costs y burles. 

 

Would you be able to arrive at cell (n,m) spending precisely k burles? 

 

Input 

 

The primary line contains the single integer t (1≤t≤100) — the number of experiments. 

 

The sole line of each experiment contains three integers n, m, and k (1≤n,m≤100; 0≤k≤104) — the spans of lattice and the specific measure of cash you wanted to spend. 

 

Output 

 

For each experiment, on the off chance that you can arrive at cell (n,m) spending precisely k burles, print YES. In any case, print NO. 

 

You might print each letter regardless you need

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