Problem Statement

There is an anemometer on the roof of Sakura High School, and the wind force of $1$ day is determined using this anemometer.

Specifically, when the propeller of the anemometer rotates $x$ times during $1$ day, the wind force of that day is defined as the integer obtained by rounding $\dfrac{x}{A}$ to the nearest integer, rounding half up at the first decimal place.

There is a record of the number of rotations of the anemometer's propeller over a certain period of $D$ consecutive days. On day $d~(1 \leq d \leq D)$, the propeller of the anemometer rotated $X_d$ times.

Find the wind force on each day.

Solve $T$ test cases.

Constraints

• $1 \leq T \leq 100$.
• Constraints for each test case
  • $1 \leq D \leq 100$.
  • $1 \leq A \leq 10^{18}$.
  • $0 \leq X_d\leq 10^{18} \quad (1 \leq d \leq D)$.
• All inputs are integers.

Input

$T$
${\rm case}_1$
$\vdots$
${\rm case}_T$

$D$ $A$
$X_1$ $X_2$ $\cdots$ $X_D$

Output

The output consists of $T$ lines. On line $t~(1 \leq t \leq T)$, output the answer to the $t$-th test case in the following format.

• Let $P_d$ be the wind force on day $d~(1 \leq d \leq D)$. Output $P_1, P_2, \dots, P_D$ on $1$ line, separated by spaces.

  Specifically, output in the following format.

  $P_1$ $P_2$ $\cdots$ $P_D$

Do not forget the newline at the end.

Sample

2
3 10
83 99 15
1 987654321
998877665544332211

8 10 2
1011363636