B. Multihedgehogtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputSomeone give a strange birthday present to Ivan. It is hedgehog — connected undirected graph in which one vertex has degree at least 3 (we will call it center) and all other vertices has degree 1. Ivan thought that hedgehog is too boring and decided to make himself k-multihedgehog.Let us define k-multihedgehog as follows: 1-multihedgehog is hedgehog: it has one vertex of degree at least 3 and some vertices of degree 1. For all k \ge 2, k-multihedgehog is (k-1)-multihedgehog in which the following changes has been made for each vertex v with degree 1: let u be its only neighbor; remove vertex v, create a new hedgehog with center at vertex w and connect vertices u and w with an edge. New hedgehogs can differ from each other and the initial gift. Thereby k-multihedgehog is a tree. Ivan made k-multihedgehog but he is not sure that he did not make any mistakes. That is why he asked you to check if his tree is indeed k-multihedgehog.InputFirst line of input contains 2 integers n, k (1 \le n \le 10^{5}, 1 \le k \le 10^{9}) — number of vertices and hedgehog parameter.Next n-1 lines contains two integers u v (1 \le u, \,\, v \le n; \,\, u \ne v) — indices of vertices connected by edge.It is guaranteed that given graph is a tree.OutputPrint "Yes" (without quotes), if given graph is k-multihedgehog, and "No" (without quotes) otherwise.ExamplesInput14 21 42 43 44 1310 511 512 514 55 136 78 613 69 6OutputYesInput3 11 32 3OutputNoNote2-multihedgehog from the first example looks like this:Its center is vertex 13. Hedgehogs created on last step are: [4 (center), 1, 2, 3], [6 (center), 7, 8, 9], [5 (center), 10, 11, 12, 13].Tree from second example is not a hedgehog because degree of center should be at least 3.
Input14 21 42 43 44 1310 511 512 514 55 136 78 613 69 6
OutputYes
['dfs and similar', 'graphs', 'shortest paths', '*1800']