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 <bits/stdc++.h>

#define rep(i, a, b) for (int i = a; i < (int)(b); ++i)
#define rrep(i, a, b) for (int i = b - 1; i >= (int)(a); --i)

using namespace std;
using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
using vd = vector<double>;
using vvi = vector<vi>;

constexpr int MOD = 1000000007;

// Data structures.
struct Point {
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}
    Point(const Point& p) : x(p.x), y(p.y) {}

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

    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) < 1e-10 && fabs(y - p.y) < 1e-10; }

    static double norm(const Point& p) { return sqrt(p.x * p.x + p.y * p.y); }
    static double dot(const Point& p1, const Point& p2) { return p1.x * p2.x + p1.y * p2.y; }
    static double cross(const Point& p1, const Point& p2) { return p1.x * p2.y - p1.y * p2.x; }
};

struct Segment {
    Point s, t;
};

double distance(const Segment& s, const Point& p) {
    return abs(Point::cross(s.t - s.s, p - s.s)) / Point::norm(s.t - s.s);
}

Point cross_point(const Segment& s1, const Segment& s2) {
    double ds = distance(s1, s2.s);
    double dt = distance(s1, s2.t);
    return s2.s + (s2.t - s2.s) * ds / (ds + dt);
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int q;
    cin >> q;

    rep(i, 0, q) {
        Segment s1, s2;
        cin >> s1.s.x >> s1.s.y >> s1.t.x >> s1.t.y;
        cin >> s2.s.x >> s2.s.y >> s2.t.x >> s2.t.y;
        Point p = cross_point(s1, s2);
        printf("%.10f %.10f\n", p.x, p.y);
    }

    return 0;
}