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B. Multihedgehog

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard 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.

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 2

1 4

2 4

3 4

4 13

10 5

11 5

12 5

14 5

5 13

6 7

8 6

13 6

9 6

Output

Yes

Input

3 1

1 3

2 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 $$$3$$$.

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