Path

Time Limit: 4000/2000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

Problem Description

Check if there exists a path of length \(l\) in the given tree with weight assigned to each edges.

Input

The first line contains two integers \(n\) and \(q\), which denote the number of nodes and queries, repectively.

The following \((n - 1)\) with three integers \(a_i, b_i, c_i\), which denote the edge between \(a_i\) and \(b_i\), with weight \(c_i\).

Note that the nodes are labled by \(1, 2, \ldots, n\).

The last line contains \(q\) integers \(l_1, l_2, \ldots, l_q\), denote the queries.

\((1 \leq n, q \leq 10^5, 1 \leq c_i \leq 2)\)

Output

For each query, print the result in seperated line. If there exists path of given length, print "Yes". Otherwise, print "No".

Sample Input

4 6
1 2 2
2 3 1
3 4 2
0 1 2 3 4 5

Sample Output

Yes
Yes
Yes
Yes
No
Yes

Source

ftiasch

Manager

Information
Solved Number40
Submit Number153
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