A functional graph is a directed graph where each node has outdegree $1$. For example, here is a functional graph that has $9$ nodes and $2$ components:
Given $n$, your task is to calculate for each $k=1 \dots n$ the number of functional graphs that have $n$ nodes and $k$ components.
Input
The only input line has an integer $n$: the number of nodes.
Output
Print $n$ lines: for each $k=1 \dots n$ the number of graphs modulo $10^9+7$.
