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B. Multihedgehog
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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.

Output

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

Examples
Input
14 21 42 43 44 1310 511 512 514 55 136 78 613 69 6
Output
Yes
Input
3 11 32 3
Output
No
Note

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 $3$.