We caught Kevin! Now we have to get a written confession out of him.

In order to do this, we need to interrogate him, where Kevin's psychological state is modelled as a coordinate on a 2D Cartesian plane. Initially Kevin is calm, starting at the origin ~(0,0)~

To extract a confession, we must drill Kevin with a series of intense questions. We have to manipulate his psychological state to reach exactly the breaking point, located at the coordinates ~(x,y)~

Every time we ask a question, Kevin's mental state shifts by exactly ~1~ unit in one of the four directions: up, down, left, or right.

Unfortunately, due to the Kiriakou Law, our interrogation must last exactly ~k~ questions. We cannot stop the interrogation early.

If Kevin reaches the breaking point before the ~k~th question, we must continue asking questions.

Given the coordinates of the breaking point ~(x,y)~ and the required number of questions ~k~, determine if it is possible for Kevin's psychological state to land exactly on ~(x,y)~ after exactly ~k~ questions.

Input

The input consists of a single line containing three integer ~x~, ~y~, and ~k~ (~-10^6 \leq x,y \leq 10^6 \; 1 \leq k \leq 2\times 10^6~)

Output

Output Yes if you can land exactly on the breaking point after ~k~ questions. Otherwise, output No.

Example

Input 1

1 1 2

Output 1

Yes

You need to reach ~(1,1)~ in exactly ~2~ questions. You can shift right to ~(1,0)~, and then shift up to ~(1,1)~ on the second, using up the ~2~ questions. Therefore, the output is Yes.

Input 2

10 0 5

Output 2

No

Clearly, the breaking point ~(10,0)~ is too far to reach in exactly ~5~ questions.

Input 3

0 3 4

Output 3

No

This time, we can reach the breaking point ~(0,3)~, but we much reach it in exactly ~4~ questions, which is impossible.