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 Int int64_t
#define dump(x) cout << (x) << endl
#define fi first
#define se second
Int mod = 1e9+7;
//Int mod = 1e6+3;

int main() {
    pair<double, double> p1, p2;
    cin >> p1.fi >> p1.se >> p2.fi >> p2.se;
    int q;
    cin >> q;
    vector<pair<double, double>> v(q);
    for (int i = 0; i < q; i++) cin >> v[i].fi >> v[i].se;
    for (int i = 0; i < q; i++) {
        if (p1.fi == p2.fi) {
            printf("%.12lf %.12lf\n", p1.fi - (v[i].fi - p1.fi), v[i].se);
        }
        else if (p1.se == p2.se) {
            printf("%.12lf %.12lf\n", v[i].fi, p1.se - (v[i].se - p1.se));
        }
        else {
            pair<double, double> x = v[i];
            double a1 = (p2.se - p1.se) / (p2.fi - p1.fi);
            double b1 = p1.se - a1 * p1.fi;
            double a2 = -1.0 / a1;            
            double b2 = x.se - a2 * x.fi;        
            double rx = (b2 - b1) / (a1 - a2);
            double ry = a1 * rx + b1;
            printf("%.12lf %.12lf\n", (rx - v[i].fi)  * 2.0 + v[i].fi, (ry - v[i].se) * 2.0 + v[i].se);
        }
    }
    return 0;
}