Behruzbek received a tree (^{\text{∗}}) with (n) nodes. For a chosen root (^{\text{†}}) (r), Behruzbek wants to find cuteness of the tree. Consider every set of (k) distinct nodes of the tree. For each such set, compute its lowest common ancestor ( LCA ) in the tree when it is rooted at (r). Let (S_r) be the set of all distinct nodes obtained this way; then cuteness of the tree is (|S_r|), where (|S|) means the number of distinct elements. After discovering the cuteness of trees, Behruzbek became interested in finding the kawaiiness of the tree! Kawaiiness is defined as: () \sum_{r = 1}^{n} |S_r| = |S_1| + |S_2| + \dots + |S_n| () Unfortunately, Behruzbek is feeling sleepy now. Please help Behruzbek by finding the kawaiiness of the tree! (^{\text{∗}})A tree is a connected graph without cycles. (^{\text{†}})A rooted tree is a tree where one vertex is special and called the root. The first line contains the number of test cases (t) ((1 \leq t \leq 10^{4})). The first line of each test case contains two integers (n) and (k) ((2 \leq k \leq n \leq 2\cdot 10^{5})) — the number of vertices in the tree and the number of distinct integers to be chosen. The following (n-1) lines of each test case describe the tree. Each of the lines contains two integers (u) and (v) ((1 \leq u,v \leq n), (u \ne v)) that indicate an edge between vertex (u) and (v). It is guaranteed that these edges form a tree. It is guaranteed that the sum of (n) over all test cases does not exceed (2\cdot 10^{5}). For each test case, output one integer — the value of (\sum\limits_{r=1}^n |S_r|). Let (f(i) = |S_i|) For the third example: Root is (1), only (1) and (2) nodes can be obtained. For example, we can choose: (LCA(4, 5, 6) = 1) and (LCA(2, 4, 5) = 2). As a result, (f(1) = 2). Root is (2), only (1) and (2) nodes can be obtained. For example,