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.

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, ..., an, where each ai 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 "xi yi" (without the quotes) (1 ≤ xi, yi ≤ n, xi ≠ yi), where xi and yi 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.

Examples

Input

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


Output

2


Input

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


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: <image> 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: <image> The restaurants are located at vertices 4, 5, 6, 7. Kefa can't go to restaurants 6, 7.
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */




import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Stack;

/**
 *
 * @author KIIT
 */
public class KefaAndPark {
  static  class Reader 
	{ 
		final private int BUFFER_SIZE = 1 << 16; 
		private DataInputStream din; 
		private byte[] buffer; 
		private int bufferPointer, bytesRead; 

		public Reader() 
		{ 
			din = new DataInputStream(System.in); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 

		public Reader(String file_name) throws IOException 
		{ 
			din = new DataInputStream(new FileInputStream(file_name)); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 

		public String readLine() throws IOException 
		{ 
			byte[] buf = new byte[64]; // line length 
			int cnt = 0, c; 
			while ((c = read()) != -1) 
			{ 
				if (c == '\n') 
					break; 
				buf[cnt++] = (byte) c; 
			} 
			return new String(buf, 0, cnt); 
		} 

		public int nextInt() throws IOException 
		{ 
			int ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do
			{ 
				ret = ret * 10 + c - '0'; 
			} while ((c = read()) >= '0' && c <= '9'); 

			if (neg) 
				return -ret; 
			return ret; 
		} 

		public long nextLong() throws IOException 
		{ 
			long ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
			if (neg) 
				return -ret; 
			return ret; 
		} 

		public double nextDouble() throws IOException 
		{ 
			double ret = 0, div = 1; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 

			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 

			if (c == '.') 
			{ 
				while ((c = read()) >= '0' && c <= '9') 
				{ 
					ret += (c - '0') / (div *= 10); 
				} 
			} 

			if (neg) 
				return -ret; 
			return ret; 
		} 

		private void fillBuffer() throws IOException 
		{ 
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
			if (bytesRead == -1) 
				buffer[0] = -1; 
		} 

		private byte read() throws IOException 
		{ 
			if (bufferPointer == bytesRead) 
				fillBuffer(); 
			return buffer[bufferPointer++]; 
		} 

		public void close() throws IOException 
		{ 
			if (din == null) 
				return; 
			din.close(); 
		} 

}
    static int ans= 0;
   static boolean visited[];
     static class Graph
    {
        int V;
        LinkedList<Integer> adjArr[];
        Graph(int V)
        {
            this.V = V;
            adjArr = new LinkedList[V];
            for(int i = 0;i<V;i++)
            {
             adjArr[i] = new LinkedList<>();   
            }
            
        }}
     static void AddEdge(Graph graph,int source,int dest)
        {
            graph.adjArr[source].add(dest);
          graph.adjArr[dest].add(source);
            
    }
     static void RecursiveDFS(Graph g,int s,int arr[],int count,int m)
             
     {
     
            if(!visited[s]){    
                
            visited[s] = true;
         if(arr[s] == 1)
             count++;
         else
             count = 0;
         if(count > m)
             return;
            Iterator<Integer> itr = g.adjArr[s].listIterator();
             if(g.adjArr[s].size()==1 && s!=0)
                 ans+=1;
                while (itr.hasNext())  
                { 
                    int v = itr.next(); 
                    if(!visited[v])
                        {
                      RecursiveDFS(g,v,arr,count,m);
                }
            }
               
     }
     } 
                  
             
     
      static void DFS( Graph graph,int s,int arr[]) 
        { 
            // Initially mark all vertices as not visited 
          visited = new boolean[graph.V]; 
          
      
            // Create a stack for DFS 
            Stack<Integer> stack = new Stack<>(); 
              
            // Push the current source node 
            stack.push(s); 
              int cnt =0;
            while(!stack.empty()) 
            { 
                // Pop a vertex from stack and print it 
                s = stack.peek(); 
                stack.pop(); 
                  
                // Stack may contain same vertex twice. So 
                // we need to print the popped item only 
                // if it is not visited. 
                if(!visited[s]) 
                { 
                    if(arr[s]==1)
                        cnt++;
                    visited[s]=(true); 
                } 
                  
                // Get all adjacent vertices of the popped vertex s 
                // If a adjacent has not been visited, then push it 
                // to the stack. 
                Iterator<Integer> itr = graph.adjArr[s].listIterator(); 
                  if(!itr.hasNext())
                  {
                      
                  }
                while (itr.hasNext())  
                { 
                    int v = itr.next(); 
                    if(!visited[v]) 
                        stack.push(v); 
                } 
                  
            } 
        }
      public static void main(String[] args) throws IOException {
          
         
        Reader sc = new Reader();
        int n = sc.nextInt();
        int m = sc.nextInt();
         visited= new boolean[n];
        int arr[] = new int[n];
         Graph g = new Graph(n);
        int i,j;
        for(i =0;i<n;i++)
            arr[i] = sc.nextInt();
     
        for(i=1;i<=n-1;i++)
        {
            int source  = sc.nextInt();
            int dest = sc.nextInt();
            if(source == dest)
                continue;
            AddEdge(g,source-1,dest-1);
        }
       
           RecursiveDFS(g,0,arr,0,m);   
//           printGraph(g);
           System.out.println(ans);
    }
      static void printGraph(Graph graph) 
    {        
        for(int v = 0; v < graph.V; v++) 
        { 
            System.out.println("Adjacency list of vertex "+ v); 
            System.out.print("head"); 
            for(Integer traverse: graph.adjArr[v]){ 
                System.out.print(" -> "+traverse); 
            } 
            System.out.println("\n"); 
        } 
}
}
