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:
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef long long lint;
typedef pair<int,int> P;
const int    INF=(int)1e9;
const int    MOD=(int)1e9+7;
const double EPS=(double)1e-10;
const int    dx[]={-1,0,0,1};
const int    dy[]={0,-1,1,0};
struct Accelerate_Cin{
    Accelerate_Cin(){
        cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);
    };
};

//幾何学テンプレート

#define equals(a,b) (fabs((a)-(b))<EPS)

//点
class Point{
public:
  double x,y;

  Point(double x = 0,double y = 0):x(x), y(y){};

  Point operator + (Point p) {return Point (x+p.x, y+p.y);}
  Point operator - (Point p) {return Point (x-p.x, y-p.y);}
  Point operator * (double a) {return Point(a*x, a*y);}
  Point operator / (double a) {return Point(x/a,y/a);}

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

  bool operator < (const Point &p)const{
    return x!=p.x ? x<p.x:y<p.y;
  }
  bool operator > (const Point &p)const{
    return x!=p.x ? x>p.x:y>p.y;
  }
  bool operator == (const Point &p)const{
    return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
  }
};

//ベクトル
typedef Point Vector;

//内積
double dot(Vector a,Vector b){
  return a.x*b.x+a.y*b.y;
}

//外積
double cross(Vector a,Vector b){
  return a.x*b.y-a.y*b.x;
}

//線分
struct Segment{Point p1,p2;};

//直線
typedef Segment Line;

//円
class Circle{
public:
  Point c;   //中心
  double r;  //半径
  Circle(Point c=Point(),double r=0.0):c(c),r(r){}
};

//多角形
typedef vector<Point> Polygon;

//線分s1と線分s2の交点を求める。

Point getCrossPoint(Segment s1,Segment s2){
  Vector base=s2.p2-s2.p1;
  double d1=abs(cross(base,s1.p1-s2.p1));
  double d2=abs(cross(base,s1.p2-s2.p1));
  double t =d1/(d1+d2);
  return s1.p1+(s1.p2-s1.p1)*t;
}


signed main(){
  int q;cin>>q;
  for(int i=0;i<q;i++){
    double x0,y0,x1,y1,x2,y2,x3,y3;cin>>x0>>y0>>x1>>y1>>x2>>y2>>x3>>y3;
    Point p0={x0,y0},p1={x1,y1},p2={x2,y2},p3={x3,y3};
    Point ans=getCrossPoint(Segment{p0,p1},Segment{p2,p3});
    cout<<fixed<<setprecision(15)<<ans.x<<" "<<ans.y<<endl;
  }

  return 0;
}