A permutation of length $n$ is an array of length $n$ containing all integers from $1$ to $n$, and all its elements are pairwise distinct.

Having grown up and played with arrays, Anton moved on to studying more interesting arrays --- permutations. While writing his thesis, he faced a very difficult task.

He has a permutation $p$ of length $n$ and an integer $k$. He decided to construct a two-dimensional array $a$ with sizes $(k+1) \times n$.

\begin{enumerate}
\item $a_{0j}=j$ for all $j$ ($1 \leq j \leq n$);
\item $a_{ij}=a_{(i-1)p_j}$ for all $i$ ($1 \leq i \leq k$) and $j$ ($1 \leq j \leq n$).
\end{enumerate}

Let $p=[5, 3, 1, 4, 2]$ and $k=3$, then we have the following array.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|} 
 \hline
 $a_{ij}$ & $j=1$ & $j=2$ & $j=3$ & $j=4$ & $j=5$ \\
 \hline\hline
 $i=0$ & $1$ & $2$ & $3$ & $4$ & $5$ \\ 
 \hline
 $i=1$ & $5$ & $3$ & $1$ & $4$ & $2$ \\
 \hline
 $i=2$ & $2$ & $1$ & $5$ & $4$ & $3$ \\
 \hline
 $i=3$ & $3$ & $5$ & $2$ & $4$ & $1$ \\
 \hline
\end{tabular}
\end{center}

For each $x$ ($1 \leq x \leq n$), he wants to know the sum of all $j$ such that $a_{ij}=x$, where $1 \leq i \leq k$. In other words, he wants to find the sum of $k$ numbers --- the indices of the number $x$ in each $a_i$.

Consider the last example. If $x=1$, the answer will be $3+2+5=10$.

After some deliberation and simple ideas, Anton managed to solve this problem quickly. Now he wants to check if you can solve it too.