You are given a rooted tree with $2^N$ nodes numbered from $0$ to $2^N - 1$. It is rooted at node $0$. For all other nodes $i$, their parent is node $j$ such that $j$<$i$ and ($i$ ^ $j$) is minimised, where ^ denotes the bitwise XOR operator .

For example, parent of node $3$ will be node $2$ as:

$3$ ^ $0 = 3$

$3$ ^ $1 = 2$

$3$ ^ $2 = 1$

Let $f(N)$ be the sum of all pairwise distances modulo $10^9+7$ for a tree with 2^N nodes, where distance between two nodes in a tree is defined as the number of edges in the shortest path between them..

$f(1) = 1$

$f(2) = 10$

Find $f(1234567654321)$.