Mancunian And Colored Tree

After a busy week at work, the residents of Manchester and Liverpool decided to go on a hike for the weekend. While walking through the forest, they came across a unique tree consisting of $n$ vertices. The vertices of the tree are numbered from $1$ to $n$.

Each vertex of the tree is assigned one of $c$ possible colors. To fight boredom, they decided to test their logical skills. The root of the tree is vertex $1$. For each vertex, they decided to find the nearest ancestor whose color matches the color of that vertex.

Input

The first line contains two integers $n$ and $c(1\le n,c\le 10^5)$ — the number of vertices in the tree and the number of possible colors.

The second line contains $n-1$ integers, where the $i$-th number indicates the parent of the $(i+1)$-th vertex.

The third line contains $n$ integers representing the colors of the vertices. The color values range from $1$ to $c$ inclusive.

Output

Print a single line with $n$ numbers, where the $i$-th number is the vertex that is the nearest ancestor of the $i$-th vertex with the same color. If such an ancestor does not exist for a vertex, print $-1$.

Examples