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 <iostream>
#include <complex>
#include <cstdio>

using namespace std;

#define REP(i,n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i,a,b) for(int i = (a); i < (int)(b); ++i)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(v) ((int)v.size())

typedef complex<double> P;

// ??????
double dot(const P& a, const P& b) {
    return real(conj(a)*b);
}

// ???p2?????????p0, p1???????????´???????°???±?????????
P projection(const P& p0, const P& p1, const P& p2) {
    // ???????????????????????´???
    P vec1 = p1 - p0;
    P vec2 = p2 - p0;
    return p0 + vec1 * dot(vec1, vec2) / dot(vec1, vec1);
}

// ???p0, p1???????????´??????????§°?????¨????????????p2??¨????§°??????
P reflection(const P& p0, const P& p1, const P& p2) {
    P proj = projection(p0, p1, p2);
    return proj - (p2 - proj);
}

// // ????????¨???P??¨??????????????????????????¢
// double norm(const P& a, const P& b) {
//     return dot(
//     return real(conj(a)*b);
// }

int main(){
    double x0, y0, x1, y1;
    int Q;

    cin >> x0 >> y0 >> x1 >> y1;
    
    P p0(x0, y0);
    P p1(x1, y1);

    cin >> Q;
    REP(q, Q) {
        double x2, y2;
        cin >> x2 >> y2;
        P p2(x2, y2);
        auto ret = reflection(p0, p1, p2);
        printf("%.10lf %.10lf\n", ret.real(), ret.imag());
    }
}