Dhinchak and her home

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Easy
Problem

Dhinchak Pooja has given you an oppurtunity to meet her as you're her biggest fan! You're at your home at location (0,0) and Dhinchak's home is located at (a,b). But since have to meet Dhanchak Pooja you decided to get tipsy to bear through it, however you lost your sense of direction in the process. So you randomly choose the direction to go in each step. You can move a unit distance in horizontal or vertical direction, i.e. you can go from position (x,y) to positions (x+1,y) , (x,y-1), (x,y+1) or (x-1,y).

As your tipsy, you don't realise where you're going, you may even accidently return to your home position also, or may arrive at (a,b) and dont even realise it. However, you somehow reach Dhinchak's house (as you're her biggest fan ofcourse!) and say that it took you S number of steps to reach there.

Find out if it is possible for you to go from you home to Dhinchak's home in exactly S steps.


Input

First line contains T test cases

For each test case,

One line of input containing three integers a,b,S

Output

If it is possible to take exactly S steps from your home to Dhincha's print "Yes" (Without Quotes) Otherwise, Print "No" (Without Quotes)


Constraints

1 <= T <= 100000

-10^9<=a,b<=10^9

1<=s<=2*10^9


Example

Input

4

0 0 2

10 15 25

0 5 1

5 5 11

Output

Yes

Yes

No

No

Explanation

1-> from (0,0) follow steps (0,0)-> (1,0) -> (0,0) in 2 steps to reach (0,0)

Time Limit: 1
Memory Limit: 256
Source Limit:
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