Tree Inside a Tree

A perfect binary tree of height $t$, $T_t$, is an undirected graph with vertices numbered 1 to $2^{t+1}-1$. For every integer $i$ with $1 \leq i \leq 2^t-1$, there is an edge between vertex $i$ and vertex $2i$, and an edge between vertex $i$ and vertex $2i+1$.

Two graphs $G$ and $H$ are isomorphic if there is a one-to-one function $f: V(G) \to V(H)$ such that for any two vertices $u$ and $v$ of $G$, $u$ and $v$ are adjacent in $G$ if and only if $f(u)$ and $f(v)$ are adjacent in $H$. Here $V(G)$ and $V(H)$ are the vertex sets of $G$ and $H$.

Count the number of ways to remove zero or more vertices and edges from $T_N$ so that the resulting graph is isomorphic to $T_K$.

The first line contains two integers $N$ and $K$, separated by a space. ($1 \leq K \leq N \leq 5000$)

On the first line, print the answer modulo $1000000007$. $1000000007$ is a prime number.