Directional Resemblance

Input

The input is a sequence of datasets. A dataset specifies a set of three-dimensional vectors, some of which are directly given in the dataset and the others are generated by the procedure described below.

Each dataset is formatted as follows.

$m$ $n$ $S$ $W$

x_1 y_1 z_1

x_2 y_2 z_2

$\dots$

x_m y_m z_m

The first line contains four integers $m$, $n$, $S$, and $W$.

The integer $m$ is the number of vectors whose three components are directly specified in the dataset. Starting from the second line, $m$ lines have the three components of $m$ vectors. The $i$-th line of which indicates the vector v_i = (x_i, y_i, z_i). All the vector components are positive integers less than or equal to $100$.

The integer $n$ is the number of vectors generated by the following procedure.

int g = S;

for (int i=m+1; i<=m+n; i++) {

x[i] = (g/7) %100 + 1;

y[i] = (g/700) %100 + 1;

z[i] = (g/70000)%100 + 1;

if( g%2 == 0 ) { g = (g/2); }

else { g = (g/2) ^ W; }

}

For i = m+1, $\dots$, m+n, the $i$-th vector v_i of the set has three components $x[i]$, $y[i]$, and $z[i]$ generated by this procedure.

Here, values of $S$ and $W$ are the parameters $S$ and $W$ given in the first line of the dataset. You may assume 1 \le S \le 10^9 and 1 \le W \le 10^9.

The total number of vectors satisfies 2 \le m+n \le 12 \times 10^4. Note that exactly the same vector may be specified twice or more in a single dataset.

A line containing four zeros indicates the end of the input. The total of m+n for all the datasets in the input never exceeds 16 \times 10^5.

Output

For each dataset, output the pair of vectors among the specified set with the smallest non-zero angle in between. It is assured that there are at least two vectors having different directions.

Vectors should be indicated by their three components. The output for a pair of vectors v_a and v_b should be formatted in a line as follows.

x_a y_a z_a x_b y_b z_b

Two vectors (x_a, y_a, z_a) and (x_b, y_b, z_b) are ordered in the dictionary order, that is, v_a < v_b if x_a < x_b, or if x_a = x_b and y_a < y_b, or if x_a = x_b, y_a = y_b and z_a < z_b. When a vector pair is output, the smaller vector in this order should be output first.

If more than one pair makes the equal smallest angle, the pair that is the smallest among them in the dictionary order between vector pairs should be output. The pair (v_i, v_j) is smaller than the pair (v_k, v_l) if v_i < v_k, or if v_i = v_k and v_j < v_l.

Examples