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.
import math
n,k=map(int,input().split())
edges=[]
for i in range(n-1):
    edges.append(tuple(map(int,input().split())))
degreelist=[]
for i in range(min(k+1,math.floor(math.log2(n))+10)):
    degreelist.append({})
degrees=degreelist[0]
for i in range(1,n+1):
    degrees[i]=0
for guy in edges:
    degrees[guy[0]]+=1
    degrees[guy[1]]+=1
small=[]
center=None
done=False
for i in range(k):
    if not done:
        small=[]
        for guy in degrees:
            if degrees[guy]==2:
                print("No")
                done=True
                break
            if degrees[guy]==3:
                small.append(guy)
                if center==None: 
                    center=guy
                elif center!=guy:
                    print("No")
                    done=True
                    break
            elif degrees[guy]>1:
                small.append(guy)
        degrees=degreelist[i+1]
        if center!=None and center not in small:
            if not done:
                print("No")
            done=True
            break
        elif len(small)==0:
            if not done:
                print("No")
            done=True
            break
        for guy in small:
            degrees[guy]=0
        for guy in edges:
            if guy[0] in degrees and guy[1] in degrees:
                degrees[guy[0]]+=1
                degrees[guy[1]]+=1
        for guy in degrees:
            if degrees[guy]>1 and degreelist[i][guy]!=degrees[guy]:
                if not done:
                    print("No")
                done=True
                break
    else:
        break
if not done:
    if len(degreelist[-1])==1:
        print("Yes")
    else:
        print("No")