题目描述

There is a $n×m$ grid. You are standing at cell $(1,1)$ and your goal is to finish at cell $(n,m)$.

You can move to the neighboring cells to the right or down. In other words, suppose you are standing at cell $(x,y)$. You can:

• move right to the cell $(x,y+1)$ — it costs $x$ yuan;
• move down to the cell $(x+1,y)$ — it costs $y$ yuan.

Can you reach cell $(n,m)$ spending exactly $k$ yuan?

输入格式

The first line contains the single integer $t (1≤t≤100)$ — the number of test cases.

The first and only line of each test case contains three integers $n$, $m$, and $k$ $(1≤n,m≤100; 0≤k≤10^4)$ — the sizes of grid and the exact amount of money you need to spend.

输出格式

For each test case, if you can reach cell $(n,m)$ spending exactly $k$ yuan, print YES. Otherwise, print NO.

样例

6 
1 1 0 
2 2 2 
2 2 3 
2 2 4 
1 4 3 
100 100 100

YES 
NO 
YES 
NO 
YES 
NO

提示

In the first test case, you are already in the final cell, so you spend $0$ yuan.

In the second, third and fourth test cases, there are two paths from $(1,1)$ to $(2,2)$: $(1,1) → (1,2) → (2,2)$ or $(1,1) → (2,1) → (2,2)$. Both costs $1+2=3$ yuan, so it’s the only amount of money you can spend.

In the fifth test case, there is the only way from $(1,1)$ to $(1,4)$ and it costs $1+1+1=3$ yuan.