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 ≥ 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 ≤ n ≤ 10^{5}, 1 ≤ k ≤ 10^{9}) — number of vertices and hedgehog parameter.

Next n-1 lines contains two integers u v (1 ≤ u,    v ≤ n;    u ≠ 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:

<image>

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.
from collections import Counter

if __name__ == '__main__':
    n, k = map(int, input().split())
    if k >= 20 or n <= 3:
        print("No")
        exit(0)
    edges = [set() for _ in range(n)]
    survived = list(range(n))
    for i in range(n-1):
        a, b = map(int, input().split())
        edges[a-1].add(b-1)
        edges[b-1].add(a-1)
    for _ in range(k):
        leaves = []
        new_survived = []
        for i in survived:
            if len(edges[i]) == 0:
                print("No")
                exit(0)
            elif len(edges[i]) == 1:
                leaves.append(i)
            else:
                new_survived.append(i)
        if len(new_survived) == 2:
            print("No")
            exit(0)
        removed = Counter()
        for i in leaves:
            nei = edges[i].pop()
            edges[nei].remove(i)
            removed[nei] += 1
        if min(removed.values()) < 3:
            print("No")
            exit(0)
        survived = new_survived
    if len(survived) == 1:
        print("Yes")
    else:
        print("No")