You are given a permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$.

The following operation will be performed $K$ times:

• For $i=1,2,\ldots,N$, simultaneously update $P_i$ to $P_{P_i}$.

Print $P$ after all operations.

The input is given from Standard Input in the following format:

$N$ $K$

$P_1$ $P_2$ $\ldots$ $P_N$

For the $P$ after all operations, print $P_1,P_2,\ldots,P_N$ in this order, separated by spaces.

• $1\leq N\leq2\times10^5$
• $1\leq K\leq10^{18}$
• $1\leq P_i\leq N\ (1\leq i\leq N)$
• $P_i\neq P_j\ (1\leq i\lt j\leq N)$
• All input values are integers.

With each operation, $P$ changes as follows:

• After the first operation, $P$ is $(2,4,3,5,6,1)$.
• After the second operation, $P$ is $(4,5,3,6,1,2)$.
• After the third operation, $P$ is $(6,1,3,2,4,5)$.

Thus, print 6 1 3 2 4 5.

Since $P_i=i$, $P$ does not change no matter how many operations are performed.