Kefa and Park

Description:

Input:

The first line contains two integers, n and m (2 ≤ n ≤ 10⁵, 1 ≤ m ≤ n) — the number of vertices of the tree and the maximum number of consecutive vertices with cats that is still ok for Kefa.

The second line contains n integers a₁, a₂, ..., a_n, where each a_i either equals to 0 (then vertex i has no cat), or equals to 1 (then vertex i has a cat).

Next n - 1 lines contains the edges of the tree in the format "x_i y_i" (without the quotes) (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i), where x_i and y_i are the vertices of the tree, connected by an edge.

It is guaranteed that the given set of edges specifies a tree.

Output:

A single integer — the number of distinct leaves of a tree the path to which from Kefa's home contains at most m consecutive vertices with cats.

Sample Input:

4 1
1 1 0 0
1 2
1 3
1 4

Sample Output:

2

Sample Input:

7 1
1 0 1 1 0 0 0
1 2
1 3
2 4
2 5
3 6
3 7

Sample Output:

2

Note:

Let us remind you that a tree is a connected graph on n vertices and n - 1 edge. A rooted tree is a tree with a special vertex called root. In a rooted tree among any two vertices connected by an edge, one vertex is a parent (the one closer to the root), and the other one is a child. A vertex is called a leaf, if it has no children.

Note to the first sample test: The vertices containing cats are marked red. The restaurants are at vertices 2, 3, 4. Kefa can't go only to the restaurant located at vertex 2.

Note to the second sample test: The restaurants are located at vertices 4, 5, 6, 7. Kefa can't go to restaurants 6, 7.