Problem: For given three points p1, p2, p, find the projection 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 projection 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 0.0000000000
0.0000000000 0.0000000000
1.0000000000 0.0000000000


Input

0 0 3 4
1
2 5


Output

3.1200000000 4.1600000000

Solution (in CPP):

Solution:
#include <iostream>
#include <algorithm>
#include <vector>
#include <cstdio>
using namespace std;

int main() {
    int x1, y1, x2, y2;
    cin >> x1 >> y1 >> x2 >> y2;
    int q;
    cin >> q;
    vector< pair<int, int> > p(q);

    for(int i = 0; i < q; i++){
        cin >> p[i].first >> p[i].second;
    } 

    if(x2-x1 == 0){
        for(int i = 0; i < q; i++){
            cout << x1 << " " << p[i].second << endl;
        }
        return 0;
    }

    double cfi, inv_cfi, cst;
    cfi = double(y2-y1)/(x2 - x1);
    //cout << cfi << endl;
    cst = y1 - cfi * x1;
    //cout << cst << endl;
    if(cfi == 0){
        for(int i = 0; i < q; i++){
            cout << p[i].first << " " << y1 << endl;
        }
        return 0;
    }

    inv_cfi = -1/cfi;
    //cout << inv_cfi << endl;

    for(int i = 0; i < q; i++){
        double cst_p, ans_x, ans_y;
        cst_p = p[i].second - inv_cfi * (p[i].first);
        //ans_x = (cst - cst_p) / inv_cfi + cfi*p[i].first/inv_cfi;
        //cout << cst_p << endl;
        ans_x = (cst_p - cst) / (cfi - inv_cfi);
        ans_y = inv_cfi*ans_x + cst_p;
        //cout << "ans_x:" << ans_x << "  ans_y:" << ans_y << endl;
        printf("%.10lf %.10lf\n", ans_x, ans_y);
    }
    
}