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.
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

public class Codeforces {

    static int MAX = -1 >>> 1;
    static long MOD = 1_000_000_007L;

    static class Graph {
        int n;
        List<Integer>[] adj;
        int[] a;
        Graph(int[] a, int n) {
            this.n = n;
            this.a = a;
            this.adj = new List[1 + n];
            for(int i = 1; i <= n; i++) {
                this.adj[i] = new ArrayList<Integer>();
            }
        }
        void addEdge(int u, int v) {
            adj[u].add(v);
            adj[v].add(u);
        }
        int bfs(boolean[] visited, int src, int m, int om) {
            // println("src = " + src + ", m = " + m);
            if(m < 0) return 0;
            visited[src] = true;
            int ans = 0;
            boolean childFound = false;
            for(int nei : adj[src]) {
                if(visited[nei]) continue;
                childFound = true;
                ans += a[src - 1] == 1 ? bfs(visited, nei, m - 1, om) : bfs(visited, nei, om, om);
            }
            if(!childFound) {
                //leaf kitchen
                if(a[src - 1] == 1 && m == 0) {
                    ans = 0;
                    // println("found kitchen at " + src + " but it has cats and we are out of patience!");
                }
                else ans = 1;       
            }
            return ans;
        }
    }
    
    static void main2() throws Exception {
        int n = ni();
        int m = ni();
        int[] a = nia(n);
        Graph g = new Graph(a, n);
        for(int i = 0; i < n - 1; i++) {
            int u = ni();
            int v = ni();
            g.addEdge(u, v);
        }
        // println(Arrays.toString(g.adj));
        int ans = g.bfs(new boolean[1 + n], 1, m, m);
        println(ans);        

    }
    //            /$$
    //           | $$
    //   /$$$$$$$| $$  /$$$$$$   /$$$$$$$ /$$$$$$$  /$$$$$$   /$$$$$$$
    //  /$$_____/| $$ |____  $$ /$$_____//$$_____/ /$$__  $$ /$$_____/
    // | $$      | $$  /$$$$$$$|  $$$$$$|  $$$$$$ | $$$$$$$$|  $$$$$$
    // | $$      | $$ /$$__  $$ \____  $$\____  $$| $$_____/ \____  $$
    // |  $$$$$$$| $$|  $$$$$$$ /$$$$$$$//$$$$$$$/|  $$$$$$$ /$$$$$$$/
    //  \_______/|__/ \_______/|_______/|_______/  \_______/|_______/

    static class Pair <L, R> {
        L first;
        R second;

        Pair(L first, R second) {
            this.first = first;
            this.second = second;
        }

        Pair(Pair<L, R> p) {
            this.first = p.first;
            this.second = p.second;
        }

        public boolean equals(Object p2) {
            if (p2 instanceof Pair) {
                return ((Pair) p2).first.equals(first) && ((Pair) p2).second.equals(second);
            }
            return false;
        }

        public String toString() {
            return "(first=" + first.toString() + ",second=" + second.toString() + ")";
        }
    }

    static class DisjointSet {
        int[] arr;
        int[] size;
        boolean enableSize = false;

        DisjointSet(int n, boolean enableSize) {
            arr = new int[n + 1];
            this.enableSize = enableSize;
            if(this.enableSize) size = new int[n + 1];
            makeSet();
        }

        void makeSet() {
            for (int i = 1; i < arr.length; i++) {
                arr[i] = i;
                if(enableSize) size[i] = 1;
            }
        }

        void union(int i, int j) {
            if (i == j)
                return;
            if (i > j) {
                i ^= j;
                j ^= i;
                i ^= j;
            }

            i = find(i);
            j = find(j);

            if (i == j)
                return;
            arr[j] = arr[i];
            if(enableSize) {
                size[i] += size[j];
                size[j] = size[i];
            }
        }

        int find(int i) {
            if (arr[i] != i) {
                arr[i] = find(arr[i]);
                if(enableSize) size[i] = size[arr[i]];
            }
            return arr[i];
        }

        int getSize(int i) {
           i = find(i);
           if(enableSize) return size[i];
           return 0;
        }

        public String toString() {
            return Arrays.toString(arr);
        }
    }

    //              /$$     /$$ /$$
    //             | $$    |__/| $$
    //  /$$   /$$ /$$$$$$   /$$| $$  /$$$$$$$
    // | $$  | $$|_  $$_/  | $$| $$ /$$_____/
    // | $$  | $$  | $$    | $$| $$|  $$$$$$
    // | $$  | $$  | $$ /$$| $$| $$ \____  $$
    // |  $$$$$$/  |  $$$$/| $$| $$ /$$$$$$$/
    //  \______/    \___/  |__/|__/|_______/


    static int diff(int a, int b) {
        return abs(a - b);
    }

    static long diff(long a, long b) {
        return abs(a - b);
    }

    static boolean isSqrt(double a) {
        double sr = Math.sqrt(a);
        return ((sr - Math.floor(sr)) == 0);
    }

    static long abs(long a) {
        return Math.abs(a);
    }

    static int abs(int a) {
        return Math.abs(a);
    }

    static int min(int ... arr) {
        int min = Integer.MAX_VALUE;
        for (int var : arr)
            min = Math.min(min, var);
        return min;
    }

    static long min(long ... arr) {
        long min = Long.MAX_VALUE;
        for (long var : arr)
            min = Math.min(min, var);
        return min;
    }

    static long max(long ... arr) {
        long max = Long.MIN_VALUE;
        for (long var : arr)
            max = Math.max(max, var);
        return max;
    }

    static int max(int... arr) {
        int max = Integer.MIN_VALUE;
        for (int var : arr)
            max = Math.max(max, var);
        return max;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    // ____________________________________________________________________________
    //|                                                                            |
    //|  /$$$$$$  /$$$$$$         /$$$$$$   /$$                /$$$$$$   /$$$$$$   |
    //| |_  $$_/ /$$__  $$       /$$__  $$ | $$               /$$__  $$ /$$__  $$  |
    //|   | $$  | $$  \ $$      | $$  \__//$$$$$$   /$$   /$$| $$  \__/| $$  \__/  |
    //|   | $$  | $$  | $$      |  $$$$$$|_  $$_/  | $$  | $$| $$$$    | $$$$      |
    //|   | $$  | $$  | $$       \____  $$ | $$    | $$  | $$| $$_/    | $$_/      |
    //|   | $$  | $$  | $$       /$$  \ $$ | $$ /$$| $$  | $$| $$      | $$        |
    //|  /$$$$$$|  $$$$$$/      |  $$$$$$/ |  $$$$/|  $$$$$$/| $$      | $$        |
    //| |______/ \______/        \______/   \___/   \______/ |__/      |__/        |
    //|____________________________________________________________________________|



    private static byte[] scannerByteBuffer = new byte[1024]; // Buffer of Bytes
    private static int scannerIndex;
    private static InputStream scannerIn;
    private static int scannerTotal;
    private static BufferedWriter printerBW;
    private static boolean DEBUG = false;

    private static int next() throws IOException { // Scan method used to scan buf
        if (scannerTotal < 0)
            throw new InputMismatchException();
        if (scannerIndex >= scannerTotal) {
            scannerIndex = 0;
            scannerTotal = scannerIn.read(scannerByteBuffer);
            if (scannerTotal <= 0)
                return -1;
        }
        return scannerByteBuffer[scannerIndex++];
    }

    static int ni() throws IOException {
        int integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static long nl() throws IOException {
        long integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static String line() throws IOException {
        StringBuilder sb = new StringBuilder();
        int n = next();
        while (isWhiteSpace(n))
            n = next();
        while (!isNewLine(n)) {
            sb.append((char) n);
            n = next();
        }
        return sb.toString();
    }

    private static boolean isNewLine(int n) {
        return n == '\n' || n == '\r' || n == -1;
    }

    private static boolean isWhiteSpace(int n) {
        return n == ' ' || isNewLine(n) || n == '\t';
    }

    static int[] nia(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = ni();
        return array;
    }

    static int[][] n2dia(int r, int c) throws Exception {
        if (r < 0 || c < 0)
            throw new Exception("Array size should be non negative");
        int[][] array = new int[r][c];
        for (int i = 0; i < r; i++)
            array[i] = nia(c);
        return array;
    }

    static long[] nla(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static float[] nfa(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        float[] array = new float[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static double[] nda(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static <T> void print(T ... str) {
        try {
            for (T ele : str)
                printerBW.append(ele.toString());
            if (DEBUG)
                flush();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }

    static <T> void println(T ... str) {
        if (str.length == 0) {
            print('\n');
            return;
        }
        for (T ele : str)
            print(ele, '\n');
    }

    static void flush() throws IOException {
        printerBW.flush();
    }

    static void close() {
        try {
            printerBW.close();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }

    public static void main(String[] args) throws Exception {
        long startPointTime = System.currentTimeMillis();
        scannerIn = System.in;
        printerBW = new BufferedWriter(new OutputStreamWriter(System.out));
        if (args.length > 0 && args[0].equalsIgnoreCase("debug")
                || args.length > 1 && args[1].equalsIgnoreCase("debug"))
            DEBUG = true;

        main2();
        long endTime = System.currentTimeMillis();
        float totalProgramTime = endTime - startPointTime;
        if (args.length > 0 && args[0].equalsIgnoreCase("time") || args.length > 1 && args[1].equalsIgnoreCase("time"))
            print("Execution time is " + totalProgramTime + " (" + (totalProgramTime / 1000) + "s)");
        close();
    }
}
