A tree is an undirected connected graph without cycles. The distance between two vertices is the number of edges in a simple path between them. Limak is a little polar bear. He lives in a tree that consists of n vertices, numbered 1 through n . Limak recently learned how to jump. He can jump from a vertex to any vertex within distance at most k . For a pair of vertices ( s , t ) we define f ( s , t ) as the minimum number of jumps Limak needs to get from s to t . Your task is to find the sum of f ( s , t ) over all pairs of vertices ( s , t ) such that s < t . The first line of the input contains two integers n and k ( 2 ≤ n ≤ 200 000 , 1 ≤ k ≤ 5 ) — the number of vertices in the tree and the maximum allowed jump distance respectively. The next n - 1 lines describe edges in the tree. The i -th of those lines contains two integers a i and b i ( 1 ≤ a i , b i ≤ n ) — the indices on vertices connected with i -th edge. It's guaranteed that the given edges form a tree. Print one integer, denoting the sum of f ( s , t ) over all pairs of vertices ( s , t ) such that s < t . In the first sample, the given tree has 6 vertices and it's displayed on the drawing below. Limak can jump to any vertex within distance at most 2 . For example, from the vertex 5 he can jump to any of vertices: 1 , 2 and 4 (well, he can also jump to the vertex 5 itself). There are pairs of vertices ( s , t ) such that s < t . For 5 of those pairs Limak would need two jumps: (1, 6), (3, 4), (3, 5), (3, 6), (5, 6) . For other 10 pairs one jump is enough. So, the answer is 5·2 + 10·1 = 20 . In the third sample, Limak can jump between every two vertices directly. There are 3 pairs of vertices ( s < t ) , so the answer is 3·1 = 3 .