Quarantine

Seolgwak is a country of $N$ cities numbered from 1 to $N$. Exactly $N-1$ roads connect pairs of cities, and every city is reachable from every other city. Every road has length $1$.

Recently, a new virus that spread from the neighboring country Gyeonggwak has become widespread in Seolgwak. Minister of Health and Welfare Geunyeong believes that long-distance travel is the largest cause of the virus spreading. She plans to lock down some cities and close the roads connected to the locked cities.

For Geunyeong, a long-distance trip is a trip whose travel distance is at least $K$ and that does not pass through the same city more than once.

For example, suppose $K = 3$ and the cities and roads are shaped as in the figure below.

A possible long-distance trip is the route that passes through cities 1, 2, 3, and 6 in order, or the route that passes through cities 5, 3, 6, and 7 in order. There are many other long-distance trips besides these.

If city 3 is locked, no route that avoids passing through the same city twice has length greater than 2, so long-distance travel becomes impossible. Locking every city also makes long-distance travel impossible.

Geunyeong wants to lock an appropriate set of cities so that long-distance travel is impossible. Count the number of ways to lock cities so that long-distance travel is impossible.

The first line contains the number of cities $N$ and the positive integer $K$ that Geunyeong has in mind. ($1 \le K \le N \le 300000$)

From the second line through the $N$-th line, each line contains two positive integers $x$ and $y$ ($1 \le x, y \le N$). This means a road connects city $x$ and city $y$.

On the first line, print the number of ways to lock cities so that long-distance travel is impossible, modulo $10^9+7$.