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 CPP):

Solution:
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <sstream>
#include <string>
#include <utility>
#include <map>
#include <memory>
#include <set>
#include <vector>
#include <deque>
#include <list>
#include <stack>
#include <queue>
#include <array>

using namespace std;

const double eps = 1e-10;

class Vector
{
public:
  double x;
  double y;

  Vector(){}
  Vector( double x, double y ) : x(x), y(y) {}

  Vector operator + ( const Vector v ) { return Vector( x + v.x, y + v.y ); }
  Vector operator - ( const Vector v ) { return Vector( x - v.x, y - v.y ); }
  Vector operator * ( const double k ) { return Vector( x * k, y * k ); }
  Vector operator / ( const double k ) { return Vector( x / k, y / k ); }
  bool operator < ( const Vector &v ) const { return x * x + y * y < v.x * v.x + v.y * v.y; }

  double abs() { return sqrt( norm() ); }
  double norm() { return x * x + y * y; }

  static double dot( Vector v1, Vector v2 ) { return v1.x * v2.x + v1.y * v2.y; }
  static double cross( Vector v1, Vector v2 ) { return v1.x * v2.y - v1.y * v2.x; }
  
  void print() { cout << fixed << setprecision(10) << x << " " << y << endl; }
};

class CrossPoint
{
public:
  Vector p0, p1, p2, p3;
  CrossPoint(){}
  CrossPoint( Vector p0, Vector p1, Vector p2, Vector p3 ) : p0(p0), p1(p1), p2(p2), p3(p3) {}
  int solve();
};

int CrossPoint::solve()
{
  Vector a = p1 - p0;
  Vector b = p3 - p2;
  Vector p = p2 - p0;

  Vector cp = p0 + a * Vector::cross( b, p ) / Vector::cross( b, a );
  cp.print();
  
  return 0;
}

int main()
{
  int q;
  cin >> q;
  
  for ( auto i = 0; i < q; ++i )
    {
      double xp0, yp0, xp1, yp1, xp2, yp2, xp3, yp3;
      cin >> xp0 >> yp0 >> xp1 >> yp1 >> xp2 >> yp2 >> xp3 >> yp3;

      CrossPoint cp(Vector(xp0, yp0), Vector(xp1, yp1), Vector(xp2, yp2), Vector(xp3, yp3));
      cp.solve();
    }

  return 0;
}