CodeForces - 1058D D. Vasya and Triangle

D. Vasya and Triangle

time limit per test1 second

memory limit per test256 megabytes

inputstandard input

outputstandard output

Vasya has got three integers n, m and k. He’d like to find three integer points (x1,y1), (x2,y2), (x3,y3), such that 0≤x1,x2,x3≤n, 0≤y1,y2,y3≤m and the area of the triangle formed by these points is equal to nmk.

Help Vasya! Find such points (if it’s possible). If there are multiple solutions, print any of them.

Input

The single line contains three integers n, m, k (1≤n,m≤109, 2≤k≤109).

Output

If there are no such points, print “NO”.

Otherwise print “YES” in the first line. The next three lines should contain integers xi,yi — coordinates of the points, one point per line. If there are multiple solutions, print any of them.

You can print each letter in any case (upper or lower).

Examples

inputCopy

4 3 3

outputCopy

YES

1 0

2 3

4 1

inputCopy

4 4 7

outputCopy

NO

Note

In the first example area of the triangle should be equal to nmk=4. The triangle mentioned in the output is pictured below:

In the second example there is no triangle with area n*m/k=16/7.

不要被他给的图迷惑，这就是个水题。

include<iostream>
using namespace std;
int main()
{
   long long  int n,m,k,i;
   cin>>n>>m>>k;
  if((n*m)%(2*k)!=0)
  {
      cout<<"NO";
      return 0;
  }
  for(i=1;i<=m;i++)
  {
      if((n*i)==(2*n*m)/k)
      {
          cout<<"YES"<<endl;
          cout<<0<<' '<<0<<endl;
          cout<<0<<' '<<n<<endl;
          cout<<n<<' '<<i<<endl;
          return 0;
      }
  }
  for(i=1;i<=n;i++)
  {
      if((m*i)==(2*n*m)/k)
      {
          cout<<"YES"<<endl;
          cout<<0<<' '<<0<<endl;
          cout<<0<<' '<<m<<endl;
          cout<<0<<' '<<i<<endl;
          return 0;
      }
  }
}