CF292-A

Someday, Drazil wanted to go on date with Varda. Drazil and Varda live on Cartesian plane. Drazil's home is located in point (0, 0) and Varda's home is located in point (a, b). In each step, he can move in a unit distance in horizontal or vertical direction. In other words, from position (x, y) he can go to positions (x + 1, y), (x - 1, y), (x, y + 1) or (x, y - 1).

Unfortunately, Drazil doesn't have sense of direction. So he randomly chooses the direction he will go to in each step. He may accidentally return back to his house during his travel. Drazil may even not notice that he has arrived to (a, b) and continue travelling.

Luckily, Drazil arrived to the position (a, b) successfully. Drazil said to Varda: "It took me exactly s steps to travel from my house to yours". But Varda is confused about his words, she is not sure that it is possible to get from (0, 0) to (a, b) in exactly s steps. Can you find out if it is possible for Varda?

Input

You are given three integers a, b, and s ( - 10⁹ ≤ a, b ≤ 10⁹, 1 ≤ s ≤ 2·10⁹) in a single line.

Output

If you think Drazil made a mistake and it is impossible to take exactly s steps and get from his home to Varda's home, print "No" (without quotes).

Otherwise, print "Yes".

Sample test(s)

input

5 5 11

output

No

input

10 15 25

output

Yes

input

0 5 1

output

No

input

0 0 2

output

Yes

Note

In fourth sample case one possible route is: $\text{[math]}$ .

给定一个目标地点(a,b)和确定步数s

问是否能走s步从(0,0)到(a,b),注:走的过程可以返回上一步

以最短路径走到目标点和多次走到目标所需的步数的奇偶性一致,故只需要判断所给步数与以最短路步数的奇偶性是否一致即可

#include <iostream>
using namespace std;
int main()
{
    int a,b,n;
    cin>>a>>b>>n;
    if(a<0)
        a=-a;
    if(b<0)
        b=-b;
    if((n-a-b)%2==0&&n-a-b>=0)
        cout<<"YES"<<endl;
    else
        cout<<"NO"<<endl;
    return 0;
}