Problem: For given two segments s1 and s2, print the coordinate of the cross point of them.

s1 is formed by end points p0 and p1, and s2 is formed by end points p2 and p3.

Constraints

* 1 ≤ q ≤ 1000
* -10000 ≤ xpi, ypi ≤ 10000
* p0 ≠ p1 and p2 ≠ p3.
* The given segments have a cross point and are not in parallel.

Input

The entire input looks like:


q (the number of queries)
1st query
2nd query
...
qth query


Each query consists of integer coordinates of end points of s1 and s2 in the following format:


xp0 yp0 xp1 yp1 xp2 yp2 xp3 yp3


Output

For each query, print the coordinate of the cross point. The output values should be in a decimal fraction with an error less than 0.00000001.

Example

Input

3
0 0 2 0 1 1 1 -1
0 0 1 1 0 1 1 0
0 0 1 1 1 0 0 1


Output

1.0000000000 0.0000000000
0.5000000000 0.5000000000
0.5000000000 0.5000000000

Solution (in JAVA):

Solution:
import java.awt.geom.Line2D;
import java.awt.geom.Point2D;
import java.util.*;
public class Main {
	Scanner in = new Scanner(System.in);
	public static void main(String[] args) {
		new Main();
	}

	public Main() {
		int q = in.nextInt();
		for(int i=0;i<q;i++)new CGL_2B().doIt();
	}



	class CGL_2B{
		double cross(Point2D p1,Point2D p2){
			return p1.getX()*p2.getY()-p1.getY()*p2.getX();
		}
		//和
		Point2D sum(Point2D p1,Point2D p2){
			return new Point2D.Double(p1.getX()+p2.getX(),p1.getY()+p2.getY());
		}
		Point2D mul(double n,Point2D p1){
			return new Point2D.Double(p1.getX()*n,p1.getY()*n);
		}
		Point2D diff(Point2D p1,Point2D p2){
			return new Point2D.Double(p1.getX()-p2.getX(),p1.getY()-p2.getY());
		}
		Point2D intersectionPoint(Line2D l1,Line2D l2){
			return intersectionPoint(l1.getP1(), l1.getP2(), l2.getP1(), l2.getP2()); 
		}
		Point2D intersectionPoint(Point2D a1,Point2D a2,Point2D b1,Point2D b2){
			Point2D a=diff(a2,a1),
					b=diff(b2,b1);
			return sum(a1, mul(cross(b, diff(b1,a1))/cross(b,a), a));
		}
		void doIt(){
			Line2D l1 = new Line2D.Double(in.nextDouble(),in.nextDouble(),in.nextDouble(),in.nextDouble());;
			Line2D l2 = new Line2D.Double(in.nextDouble(),in.nextDouble(),in.nextDouble(),in.nextDouble());;
			Point2D p = intersectionPoint(l1, l2);
			System.out.printf("%.10f %.10f\n",p.getX(),p.getY());
		}
	}


}