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 <cmath>
#include <complex>
#include <tuple>
using namespace std;

using vec = complex<double>;
using line = pair<vec,vec>;
const double eps = 0.0000001;

double inner_product(vec u,vec v){
    return real(u*conj(v));
}
double cross_product(vec u,vec v){
    return imag(conj(u)*v);
}

double norm(vec& u){
    return abs(u);
}

vec projection(line l,vec p){//p???l???????°???±
    vec s=l.first, t=l.second;
    double k = inner_product(t-s,p-s)/inner_product(t-s,t-s);
    return (1.0-k)*s+k*t;
}

vec reflection(line l,vec p){
    return 2.0*projection(l,p)-p;
}

int ccw(vec& a, vec& b, vec& c){
    vec ab = b-a, ac = c-a;
    double o = cross_product(ab,ac);
    if(o>0) return 1; //CCW
    if(o<0) return -1; //CW
    if(inner_product(ab,ac)<0){
        return 2; //C-A-B
    }else{
        if(inner_product(ab,ab)<inner_product(ac,ac)){
            return -2; //A-B-C
        }else{
            return 0; //A-C-B
        }
    }
}

bool isIntersect(line l0, line l1){
    int s = ccw(l0.first,l0.second,l1.first)*ccw(l0.first,l0.second,l1.second);
    if(s!=0&&s!=-1&&s!=-4) return false;
    s=ccw(l1.first,l1.second,l0.first)*ccw(l1.first,l1.second,l0.second);
    if(s!=0&&s!=-1&&s!=-4) return false;
    else return true;
}

vec interSection(line l0, line l1){
    vec s0, t0, s1, t1;
    tie(s0,t0)=l0; tie(s1,t1)=l1;
    double k = cross_product(t1-s1,s1-s0)/cross_product(t1-s1,t0-s0);
    return s0+(t0-s0)*k;
}

//???????????§???????????????

int main(void){
    int q;
    cin >> q;
    cout.precision(10);
    cout << fixed;
    while(q--){
        int x,y;
        cin>>x>>y;
        vec s0(x,y);
        cin>>x>>y;
        vec t0(x,y);
        cin>>x>>y;
        vec s1(x,y);
        cin>>x>>y;
        vec t1(x,y);
        vec v = interSection(line(s0,t0),line(s1,t1));
        cout << v.real() << " " << v.imag() << endl;
    }
    return 0;
}