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>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define rep(i,n) for(int i=0;i<n;++i)

using namespace std;

typedef pair<int,int>P;
typedef pair<double,double>pdd;

const int MAX_N = 100005;

int Q;

pdd projection(P p1,P p2,P p)
{
	P a = P(p2.first-p1.first,p2.second-p1.second);
	P b = P(p.first - p1.first,p.second - p1.second);
	double sa = sqrt(a.first*a.first + a.second*a.second);
	double sb = sqrt(b.first*b.first + b.second*b.second);
	double rt = (a.first*b.first+a.second*b.second)/(sa*sa);
	return pdd(p1.first+rt*a.first,p1.second+rt*a.second);
}

int main()
{
	P p1,p2,p;
	scanf("%d%d%d%d",&p1.first,&p1.second,&p2.first,&p2.second);
	scanf("%d",&Q);
	rep(i,Q){
		pdd res;
		scanf("%d%d",&p.first,&p.second);
		res = projection(p1,p2,p);
		printf("%.10f %.10f\n",2*res.first - p.first,2*res.second - p.second);
	}
	return 0;
}