12871287 SUSTech Online Judge
Problem 1287 --The Sword of Damocles

## 1287: The Sword of Damocles

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 923  Solved: 184
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## Description

One day, an elder told Pisces that there was a legendary sword at the end of the sky - the sword of Damocles. Pisces decided to get the sword at any cost. The area between Pisces and the sword can be described as a rectangular field of $$n*m$$ square meters, with Pisces currently at the top left corner and the sword at the bottom right corner. However, $$k$$ monsters are living in this area, and to keep himself safe, Pisces must keep a distance longer than $$S_i$$ from the $$i$$-th monster (Euclidean Distance). Given the locations of these $$k$$ monsters, Pisces wants to find whether he can get the legendary sword.

## Input

The first line of input contains an integer $$T$$ $$(1\leq T \leq 10)$$, which denotes the number of test cases.

For each of the test case, the first line contains three integers, $$N$$, $$M$$, and $$K$$ $$(10 ≤ N, M ≤ 10^4 , 1 ≤ K ≤ 1000)$$. Pisces is now at position $$(0, 0)$$, and the sword at position $$(N, M)$$. Each of the next $$K$$ lines describes one of the $$K$$ monsters, it contains three integers, $$X, Y,$$ and $$S$$, where $$(X, Y)$$ represents the location and $$S$$ represents the distance that must be kept. $$(0\leq X\leq N, 0\leq Y\leq M, 0 < S ≤ 10^4 )$$.

## Output

For each test case, print “Yes” if Pisces can get the sword, and “No” otherwise.

## Sample Input

1
10 10 2
3 7 4
5 4 4

## Sample Output

No

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