Tree Country

Tree Country has $N$ cities, numbered 1 to $N$. Its road network forms a tree. That is, there are $N-1$ two-way roads and every city is connected, so you can always travel between any two cities.

$K$ employees of one company are moving to Tree Country. Every employee must live in a different city, so you have to pick $K$ cities. One condition applies: the cities where the employees live must be connected to one another. If two employees live in cities $i$ and $j$, then every city on the path between $i$ and $j$ must also have an employee living in it.

Given the tree structure of Tree Country, write a program that counts the ways to pick the $K$ cities.

The first line contains the number of cities $N$ and the number of employees $K$, separated by a space. ($2 \le N \le 50$, $1 \le K \le N$)

Each of the next $N-1$ lines describes one road with the numbers $u$ and $v$ of the two cities it joins. ($1 \le u, v \le N$, $u \ne v$) The $N-1$ roads form a tree.

Print the number of ways to pick the $K$ cities, modulo 1,000,000,007.