CF580C.Kefa and Park

Kefa decided to celebrate his first big salary by going to the restaurant.

He lives by an unusual park. The park is a rooted tree consisting of n vertices with the root at vertex 1. Vertex 1 also contains Kefa's house. Unfortunaely for our hero, the park also contains cats. Kefa has already found out what are the vertices with cats in them.

The leaf vertices of the park contain restaurants. Kefa wants to choose a restaurant where he will go, but unfortunately he is very afraid of cats, so there is no way he will go to the restaurant if the path from the restaurant to his house contains more than m consecutive vertices with cats.

Your task is to help Kefa count the number of restaurants where he can go.

Kefa 决定用自己第一笔丰厚的薪水去餐馆庆祝。

他住在一座特殊的公园旁。这座公园是一棵以顶点 1 为根的有根树，包含 $n$ 个顶点，而顶点 1 也是 Kefa 的家所在位置。不幸的是，这座公园里还生活着猫。Kefa 已经查明了哪些顶点上有猫。

公园的叶顶点处设有餐馆。Kefa 想选择一家餐馆前往，但不幸的是，他非常怕猫，因此如果从某家餐馆到他家的路径上存在超过 $m$ 个连续的、有猫的顶点，则他绝不会去这家餐馆。

你的任务是帮助 Kefa 计算出他可以前往的餐馆数量。

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 _a_1, _a_2, ..., 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.

第一行包含两个整数 $n$ 和 $m$（$2 \leq n \leq 10^5$，$1 \leq m \leq n$）—— 分别表示树的顶点数以及 Kefa 能够接受的连续有猫顶点的最大数目。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$，其中每个 $a_i$ 要么为 $0$（表示顶点 $i$ 没有猫），要么为 $1$（表示顶点 $i$ 有一只猫）。

接下来 $n-1$ 行，每行描述树的一条边，格式为 “$x_i\ y_i$”（不含引号）（$1 \leq x_i, y_i \leq n$，$x_i \neq y_i$），其中 $x_i$ 和 $y_i$ 是由该边连接的两个顶点。

保证所给的边集构成一棵树。

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.

一个整数——从基法家出发到该叶子的路径上，最多包含 m 个连续的、有猫的顶点的树的不同叶子节点的数量。

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.

我们提醒您，树是一种包含 $n$ 个顶点和 $n-1$ 条边的连通图。有根树是一种指定某个特殊顶点作为根的树。在有根树中，任意两个由一条边相连的顶点之间，其中一个顶点是父节点（即离根更近的那个），另一个是子节点。若一个顶点没有子节点，则称其为叶子节点。

第一个样例测试说明： 标记为红色的顶点表示该处有猫。餐馆位于顶点 2、3、4。Kefa 只能前往顶点 2 处的餐馆（即无法前往其余餐馆）。

第二个样例测试说明： 餐馆位于顶点 4、5、6、7。Kefa 无法前往位于顶点 6 和 7 的餐馆。