Problem Statement

There are $N$ classrooms and $N$ students, each numbered from $1$ to $N$. Initially, student $i(1 \leq i \leq N)$ is in classroom $A_i$, and $(A_1,A_2,\ldots,A_N)$ is a permutation of $(1,2,\ldots,N)$. You are given $N,A,$ and a prime number greater than $\color{red}{N}$, denoted by $p$. Construct $1$ sequence $B$ that satisfies all of the following. (It is guaranteed that such a sequence always exists.)

• $B$ is an integer sequence of length $N$, and $1 \leq B_i \leq N$ holds for $i=1,2,\ldots ,N$.
• After repeating the following $\color{red}{2p}$ times, the number of $i(1 \leq i \leq N)$ such that student $i$ is not in classroom $i$ is less than $\sqrt{N}$.
• For all $i=1,2,\ldots,N$, if student $i$ is in classroom $j$, teleport the student to classroom $B_j$.

Constraints

• All input values are integers
• $1 \leq T \leq 100$
• $2 \leq N \leq 10^4$
• $N \lt p \leq 2 \times 10^4$
• $(A_1,A_2,\ldots,A_N)$ is a permutation of $(1,2,\ldots,N)$

Input

$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$

$N\ p$
$A_1\ A_2\ \ldots\ A_N$

Output

Print $T$ lines. On the $t(1 \leq t \leq T)$-th line, print the sequence $B_1,B_2,\ldots,B_N$ for the $t$-th test case, separated by spaces.

Sample

2
3 5
2 1 3
5 7
1 3 2 4 5

1 1 3
1 2 2 4 5