Restore the Original (Large)

There are $N$ cards, each labeled with one of the numbers $P_1, P_2, \cdots, P_N$.

There is a sequence $D_1, D_2, \cdots, D_i, \cdots, D_N$ containing each number from 1 to N exactly once. For each $i$, taking the $D_i$-th card to the $i$-th position is called a shuffle.

For example, suppose $P_1, P_2, \cdots, P_N$ is 1, 4, 5, 3, 2 and $D_1, D_2, \cdots, D_N$ is 4, 3, 1, 2, 5. Shuffling these cards once gives 3, 5, 1, 4, 2. This is shown in the figure below. $S$ below denotes the state after shuffling the cards once.

Given the state of the cards after shuffling them $K$ times in this way and the values of $D$, find the arrangement the cards originally had.

The first line gives the number of cards $N$ and the number of shuffles $K$, separated by a space.

The second line gives $N$ values $S_i$ separated by spaces, representing the arrangement of the cards after shuffling them $K$ times.

The third line gives $N$ values $D_i$ separated by spaces.

Print the values of the original card arrangement, $P_1$ through $P_N$, separated by spaces.

• $1 \le N \le 10^6$
• $1 \le K \le 10^{15}$
• $1 \le D_i \le N$
• $1 \le P_i, S_i \le 10^6$
• $P_i$ is an integer