After a hectic week at work, Mancunian and Liverbird decide to go on a fun weekend camping trip. As they were passing through a forest, they stumbled upon a unique tree of $n$ nodes. Vertices are numbered from $1$ to $n$. Each node of the tree is assigned a color (out of $c$ possible colors). Being bored, they decide to work together (for a change) and test their reasoning skills. The tree is rooted at vertex $1$. For each node, they want to find its closest ancestor having the same color. \InputFile The first line contains two integers $n$ and $c~(1 \le n, c \le 10^5)$ denoting the number of vertices in the tree and the number of possible colors. The second line contains $n - 1$ integers. The $i$-th integer denotes the parent of the $i + 1$ - th vertex. The third line contains $n$ integers, denoting the colors of the vertices. Each color lies between $1$ and $c$ inclusive. \OutputFile Print $n$ integers. The $i$-th integer is the vertex number of lowest ancestor of the $i$-th node which has the same color. If there is no such ancestor, print $-1$ for that node.