描述

"K-Dimensional Foil" is a dimensional weapon. Its function is quite easy: It can ascend a region in 3D space to K (K≥3) dimension. One can use it to give the enemy unexpected attack. It was called "The Ultimate Weapon".

--"Remembrance of Mars's Past"

You are the chief technology officer in the space fleet, and your fleet was just suffered from the attack of the K-Dimensional Foil. The good news was that you have found the key parameter K, the dimension of the space. But staying in high dimensional space is very dangerous, you must destroy the K-Dimensional Foil as fast as possible.

You have n spaceships, spaceship i locates at s_i = (s_i,1, …, s_i,K), and the K-Dimensional  Foil is a 1-norm ball with center c = (c₁, …, c_K) and radius r, a 1-norm ball with center c and radius r is a point set defined as
{x |  d(x, c)  ≤ r}, d(x, c) =∑| x_i - c_i |

In the formula above, the coordinate of point x is (x₁, x₂ … x_K)

Your spaceships will fire laser cannon to destroy the K-Dimensional Foil. The energy decay is very quick with the increase of the distance in the high dimensional space, so for every spaceship, you want to find the closest point (in Euclidean distance) on the K-Dimensional Foil. It's guaranteed that no spaceship is in the K-Dimensional Foil initially.

输入

The first line of the input is an integer T (T ≤ 100), the number of the test cases.

For each test case, the first line contains two integer n, K (1 ≤ n ≤ 50, 1 ≤ K ≤ 100), the number of spaceship in your fleet and the dimension of the space.

Then one line contains an integer r (1 ≤ r ≤ 10⁴ ), the radius of the K-Dimensional Foil.

Then one line contains K integers c₁, … c_K, meaning the coordinate of the center of the K-Dimensional Foil.

Then n lines follow. Each line contains K integers s_i,1, …, s_i,K, meaning the coordinate of a spaceship.

All the absolute values of the coordinate are smaller than 10⁴.

输出

For each test case, output n lines. The i^th line contains K numbers representing the coordinate of the closest point on the K-Dimensional Foil to the i^th spaceship. The absolute error between your output and the answer should be less than 10^-4

提示

The K-Dimensional Foil in the sample was a square with vertex: (1,0), (0,1), (-1,0), (0,-1)

This problem is special judged.