Problem: For given three points p1, p2, p, find the reflection point x of p onto p1p2.

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Constraints

* 1 ≤ q ≤ 1000
* -10000 ≤ xi, yi ≤ 10000
* p1 and p2 are not identical.

Input


xp1 yp1 xp2 yp2
q
xp0 yp0
xp1 yp1
...
xpq−1 ypq−1


In the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p.

Output

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

Examples

Input

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


Output

-1.0000000000 -1.0000000000
0.0000000000 -1.0000000000
1.0000000000 -1.0000000000


Input

0 0 3 4
3
2 5
1 4
0 3


Output

4.2400000000 3.3200000000
3.5600000000 2.0800000000
2.8800000000 0.8400000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
struct point {
    double x, y;
    point (){}
    point (double x, double y) : x(x), y(y){}
    point friend operator - (point l, point r) {
        return point (l.x - r.x, l.y - r.y);
    }
    point friend operator + (point l, point r) {
        return point (l.x + r.x, l.y + r.y);
    }
    double friend operator * (point l, point r) {
        return l.x * r.x + l.y * r.y;
    }
    double friend operator ^ (point l, point r) {
        return l.x * r.y - l.y * r.x;
    }
    double len () {
        return sqrt (x * x + y * y);
    }
} A, B, C, D, E;
int main () {
//    freopen ("in.txt", "r", stdin);
    int Q;
    double x1, y1, x2, y2;
    cin >> A.x >> A.y >> B.x >> B.y;
    C = B - A;
    cin >> Q;
    while (Q --) {
        cin >> D.x >> D.y;
        E = D;
        D = D - A;
        double u = C * D;
        u /= C.len () * C.len ();
        D = C;
        D.x *= u, D.y *= u;
        D = D + A;
//        cout << D.x << ' ' << D.y << endl;
        D = D - E;
        D.x *= 2, D.y *= 2;
        printf ("%.10f %.10f\n", D.x + E.x, D.y + E.y);
    }
    return 0;
}