Problem: For given a circle $c$ and a line $l$, print the coordinates of the cross points of them.

Constraints

* $p1$ and $p2$ are different
* The circle and line have at least one cross point
* $1 \leq q \leq 1,000$
* $-10,000 \leq cx, cy, x1, y1, x2, y2 \leq 10,000$
* $1 \leq r \leq 10,000$

Input

The input is given in the following format.

$cx\; cy\; r$
$q$
$Line_1$
$Line_2$
:
$Line_q$


In the first line, the center coordinate of the circle and its radius are given by $cx$, $cy$ and $r$. In the second line, the number of queries $q$ is given.

In the following $q$ lines, as queries, $Line_i$ are given ($1 \leq i \leq q$) in the following format.

$x_1\; y_1\; x_2\; y_2$

Each line is represented by two points $p1$ and $p2$ which the line crosses. The coordinate of $p1$ and $p2$ are given by ($x1$, $y1$) and ($x2$, $y2$) respectively. All input values are given in integers.

Output

For each query, print the coordinates of the cross points in the following rules.

* If there is one cross point, print two coordinates with the same values.
* Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.



The output values should be in a decimal fraction with an error less than 0.000001.

Example

Input

2 1 1
2
0 1 4 1
3 0 3 3


Output

1.00000000 1.00000000 3.00000000 1.00000000
3.00000000 1.00000000 3.00000000 1.00000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

#define _overload(_1,_2,_3,name,...) name
#define _rep(i,n) _range(i,0,n)
#define _range(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload(__VA_ARGS__,_range,_rep,)(__VA_ARGS__)

#define _rrep(i,n) _rrange(i,n,0)
#define _rrange(i,a,b) for(int i=int(a)-1;i>=int(b);--i)
#define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__)

#define _all(arg) begin(arg),end(arg)
#define uniq(arg) sort(_all(arg)),(arg).erase(unique(_all(arg)),end(arg))
#define getidx(ary,key) lower_bound(_all(ary),key)-begin(ary)
#define clr(a,b) memset((a),(b),sizeof(a))
#define bit(n) (1LL<<(n))
#define popcount(n) (__builtin_popcountll(n))

using namespace std;

template<class T>bool chmax(T &a, const T &b) { return (a<b)?(a=b,1):0;}
template<class T>bool chmin(T &a, const T &b) { return (b<a)?(a=b,1):0;}

using ll=long long;
using R=long double;
const R EPS=1e-9L; // [-1000,1000]->EPS=1e-8 [-10000,10000]->EPS=1e-7
inline int sgn(const R& r){return(r > EPS)-(r < -EPS);}
inline R sq(R x){return sqrt(max(x,0.0L));}

const int dx[8]={1,0,-1,0,1,-1,-1,1};
const int dy[8]={0,1,0,-1,1,1,-1,-1};

// Description: ????????????
// Verifyed: various problem 
const R INF = 1E40L;
const R PI = acos(-1.0L);
using P=complex<R>;
const P O=0.0L;
using L=struct{P s,t;};
using VP=vector<P>;
using C=struct{P c;R r;};

istream& operator >> (istream& is,P& p){ R x,y;is >> x >> y; p=P(x,y); return is;}
ostream& operator << (ostream& os,P& p){ os << real(p) << " " << imag(p); return os;}

inline R dot(P o,P a,P b){return real(conj(a-o)*(b-o));}
inline R det(P o,P a,P b){return imag(conj(a-o)*(b-o));}
inline int sdot(P o,P a,P b){return sgn(dot(o,a,b));}
inline int sdet(P o,P a,P b){return sgn(det(o,a,b));}

//projection verify AOJ CGL_1_A
P proj(L l,P p){ R u=real((p-l.s)/(l.t-l.s)); return (1-u)*l.s+u*l.t;}


// Circle // verified: AOJ 1183 
enum RCC{OUT=2,ON_OUT=1,ISC=0,ON_IN=-1,IN=-2};
int rcc(C a,C b){ R d=abs(a.c-b.c);return sgn(d-a.r-b.r)+sgn(d-abs(a.r-b.r));}


// cross point between circle and line 
// verified: AOJ CGL_7_D
P cir(C c,R t){return c.c+polar(c.r,t);}
VP cross(C c, L l){
	P h=proj(l,c.c),e=polar(sq(norm(c.r)-norm(h-c.c)),arg(l.t-l.s));
	return VP{h-e,h+e};
}

int main(void){
	int q;
	C c;
	cin >> c.c >> c.r;
		
	cin >> q;
	cout.precision(20);
	rep(i,q){
		P a,b;
		cin >> a >> b;
		L l={a,b};
		VP res=cross(c,l);
		if(sgn(real(res[0])-real(res[1])>0)) swap(res[0],res[1]);
		if(sgn(real(res[0])-real(res[1]))==0 and sgn(imag(res[0])-imag(res[1]))>0) swap(res[0],res[1]);
		cout << fixed << res[0] << " " << res[1] << endl;
	}
	return 0;
}