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;
#define rep(i, n) for (int i = 0; i < n; i++)

struct point {
    double x, y;
    point(double a, double b) {
        x = a, y = b;
    }
    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 k) {
        return point(k * x, k * y) ;
    }
    point operator / (double k) {
        return point(x / k, y / k);
    }
    double norm() {
        return x * x + y * y;
    }
    double abs() {
        return sqrt(norm());
    }
};

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

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

point project(point a, point base) {
    return base * (dot(a, base) / base.norm());
}

int main() {
    int x1, y1, x2, y2;
    scanf("%d %d %d %d", &x1, &y1, &x2, &y2);
    point p1(x1, y1);
    point p2(x2, y2);
    point base = p2 - p1;
    int n;
    scanf("%d", &n);
    rep(i, n) {
        int x, y;
        scanf("%d %d", &x, &y);
        point p(x, y);
        point hypo = p - p1;
        point m = p1 + project(hypo, base);
        point r = p + (m - p) * 2;
        printf("%.10lf %.10lf\n", r.x, r.y);
    }
}