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 java.io.*;
import java.util.*;

public class CF1068E extends PrintWriter {
	CF1068E() { super(System.out, true); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1068E o = new CF1068E(); o.main(); o.flush();
	}

	void main() {
		int n = sc.nextInt();
		int k = sc.nextInt();
		int[] dd = new int[n];
		int[] aa = new int[n];
		for (int h = 0; h < n - 1; h++) {
			int i = sc.nextInt() - 1;
			int j = sc.nextInt() - 1;
			dd[i]++; aa[i] ^= j;
			dd[j]++; aa[j] ^= i;
		}
		int[] kk = new int[n];
		int[] qu = new int[n]; int head = 0, cnt = 0;
		int o = -1;
		for (int i = 0; i < n; i++)
			if (dd[i] == 1) {
				kk[i] = k;
				qu[cnt++] = i;
			} else if (dd[i] <= 3) {
				if (dd[i] < 3 || o != -1) {
					println("No");
					return;
				}
				o = i;
			}
		while (n-- > 0) {
			if (cnt == 0) {
				println("No");
				return;
			}
			int i = qu[head++]; cnt--;
			if (n > 0) {
				if (dd[i] != 1 || kk[i] == 0) {
					println("No");
					return;
				}
				int j = aa[i];
				dd[j]--; aa[j] ^= i;
				k = kk[i] - 1;
				if (kk[j] == 0)
					kk[j] = k;
				if (kk[j] != k) {
					println("No");
					return;
				}
				if (dd[j] == 1)
					qu[head + cnt++] = j;
			} else {
				if (dd[i] != 0 || kk[i] != 0 || o != -1 && o != i) {
					println("No");
					return;
				}
			}
		}
		println("Yes");
	}
}
