B'You are given a tree G with n vertices and an integer k . The vertices of the tree are numbered from 1 to n . For a vertex r and a subset S of vertices of G , such that |S| = k , we define f(r, S) as the size of the smallest rooted subtree containing all vertices in S when the tree is rooted at r . A set of vertices T is called a rooted subtree, if all the vertices in T are connected, and for each vertex in T , all its descendants belong to T . You need to calculate the sum of f(r, S) over all possible distinct combinations of vertices r and subsets S , where |S| = k . Formally, compute the following: sum_{r in V} sum_{S subseteq V, |S| = k} f(r, S), where V is the set of vertices in G . Output the answer modulo 10^9 + 7 . The first line contains two integers n and k ( 3 <= n <= 2 cdot 10^5 , 1 <= k <= n ). Each of the following n - 1 lines contains two integers x and y ( 1 <= x, y <= n ), denoting an edge between vertex x and y . It is guaranteed that the given edges form a tree. Print the answer modulo 10^9 + 7 . The tree in the second example is given below: We have 21 subsets of size 2 in the given tree. Hence, S in <= ft { {1, 2 }, {1, 3 }, {1, 4 }, {1, 5 }, {1, 6 }, {1, 7 }, {2, 3 }, {2, 4 }, {2, 5 }, {2, 6 }, {2, 7 }, {3, 4 }, {3, 5 }, {3, 6 }, {3, 7 }, {4, 5 }, {4, 6 }, {4, 7 }, {5, 6 }, {5, 7 }, {6, 7 } right }. And since we have 7 vertices, 1 <= r <= 7 . We need to find the sum of f(r, S) over all possible pairs of r and S . Below we have listed the value of f(r, S) for some combinations of r and S . '...