CF1067B.Multihedgehog

Someone 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.

有人送给了伊万一个奇怪的生日礼物：一只“刺猬图”——一种连通的无向图，其中恰好有一个顶点的度数至少为 $3$（我们称其为中心），其余所有顶点的度数均为 $1$。伊万觉得刺猬图太无聊了，于是决定为自己构造一只 $k$-重刺猬图（$k$-multihedgehog）。

我们递归地定义 $k$-重刺猬图如下：

• $1$-重刺猬图即为刺猬图：它包含一个度数至少为 $3$ 的顶点，以及若干个度数为 $1$ 的顶点；
• 对任意 $k \ge 2$，$k$-重刺猬图是由 $(k-1)$-重刺猬图经过如下变换得到的：对每个度数为 $1$ 的顶点 $v$，设其唯一邻接顶点为 $u$；移除顶点 $v$，新建一只刺猬图，将其中心设为新顶点 $w$，并添加一条连接 $u$ 与 $w$ 的边。这些新加入的刺猬图彼此之间可以不同，也可以与初始礼物不同。

因此，$k$-重刺猬图是一棵树。伊万已构造出一棵 $k$-重刺猬图，但他不确定自己是否犯了错误。因此，他请你帮忙验证：他所构造的这棵树是否确实是一只 $k$-重刺猬图。

First 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.

输入的第一行包含两个整数 $n$ 和 $k$（$1 \le n \le 10^{5}$，$1 \le k \le 10^{9}$）——分别为顶点数和刺猬参数。

接下来的 $n-1$ 行每行包含两个整数 $u$ 和 $v$（$1 \le u, \,\, v \le n$；$u \ne v$）——表示由一条边连接的两个顶点的编号。

保证给定的图是一棵树。

Print "Yes" (without quotes), if given graph is $k$-multihedgehog, and "No" (without quotes) otherwise.

如果给定的图是 $k$-多重刺猬图，则输出 "Yes"（不带引号）；否则输出 "No"（不带引号）。

2-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 $3$.

第一个样例中的 2-多重刺猬图如下所示：

其中心顶点为 $13$。最后一步构造出的刺猬图分别为：

4\text{（中心）},\ 1,\ 2,\ 3$$， $$6\text{（中心）},\ 7,\ 8,\ 9$$， $$5\text{（中心）},\ 10,\ 11,\ 12,\ 13$$。 第二个样例中的树不是刺猬图，因为其中心顶点的度数至少应为 $3$。