Problem: You are given a weighted tree consisting of n vertices. Recall that a tree is a connected graph without cycles. Vertices u_i and v_i are connected by an edge with weight w_i.

You are given m queries. The i-th query is given as an integer q_i. In this query you need to calculate the number of pairs of vertices (u, v) (u < v) such that the maximum weight of an edge on a simple path between u and v doesn't exceed q_i.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5) — the number of vertices in the tree and the number of queries.

Each of the next n - 1 lines describes an edge of the tree. Edge i is denoted by three integers u_i, v_i and w_i — the labels of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i) and the weight of the edge (1 ≤ w_i ≤ 2 ⋅ 10^5). It is guaranteed that the given edges form a tree.

The last line of the input contains m integers q_1, q_2, ..., q_m (1 ≤ q_i ≤ 2 ⋅ 10^5), where q_i is the maximum weight of an edge in the i-th query.

Output

Print m integers — the answers to the queries. The i-th value should be equal to the number of pairs of vertices (u, v) (u < v) such that the maximum weight of an edge on a simple path between u and v doesn't exceed q_i.

Queries are numbered from 1 to m in the order of the input.

Examples

Input


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


Output


21 7 15 21 3 


Input


1 2
1 2


Output


0 0 


Input


3 3
1 2 1
2 3 2
1 3 2


Output


1 3 3 

Note

The picture shows the tree from the first example: <image>

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author aryssoncf
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        GPathQueries solver = new GPathQueries();
        solver.solve(1, in, out);
        out.close();
    }

    static class GPathQueries {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt(), m = in.readInt();
            int[] U = new int[n - 1], V = new int[n - 1], W = new int[n - 1];
            in.readIntArrays(U, V, W);
            MiscUtils.decreaseByOne(U, V);
            int[] order = ArrayUtils.order(W);
            long[] joined = new long[n - 1];
            ListIndependentSetSystem iss = new ListIndependentSetSystem(n);
            for (int i = 0; i < n - 1; i++) {
                int u = iss.get(U[order[i]]), v = iss.get(V[order[i]]);
                if (u == v) {
                    continue;
                }
                long res = (long) iss.getSize(u) * iss.getSize(v);
                iss.join(u, v);
                joined[i] = res;
            }
            long[] psum = ArrayUtils.partialSums(joined);
            for (int i = 0; i < m; i++) {
                int q = in.readInt(), pos = (int) MiscUtils.binarySearch(0, n - 1, x -> x == n - 1 || W[order[(int) x]] > q);
                long res = psum[pos];
                out.print(res, "");
            }
            out.printLine();
        }

    }

    static interface IndependentSetSystem {
        interface Listener {
            void joined(int joinedRoot, int root);

        }

    }

    static interface IntComparator {
        int compare(int first, int second);

    }

    static interface IntList extends IntReversableCollection {
        public abstract int get(int index);

        public abstract void set(int index, int value);

        public abstract void addAt(int index, int value);

        public abstract void removeAt(int index);

        default public void swap(int first, int second) {
            if (first == second) {
                return;
            }
            int temp = get(first);
            set(first, get(second));
            set(second, temp);
        }

        default public IntIterator intIterator() {
            return new IntIterator() {
                private int at;
                private boolean removed;

                public int value() {
                    if (removed) {
                        throw new IllegalStateException();
                    }
                    return get(at);
                }

                public boolean advance() {
                    at++;
                    removed = false;
                    return isValid();
                }

                public boolean isValid() {
                    return !removed && at < size();
                }

                public void remove() {
                    removeAt(at);
                    at--;
                    removed = true;
                }
            };
        }

        default public void add(int value) {
            addAt(size(), value);
        }

        default public IntList sort(IntComparator comparator) {
            Sorter.sort(this, comparator);
            return this;
        }

        default public IntList subList(final int from, final int to) {
            return new IntList() {
                private final int shift;
                private final int size;

                {
                    if (from < 0 || from > to || to > IntList.this.size()) {
                        throw new IndexOutOfBoundsException("from = " + from + ", to = " + to + ", size = " + size());
                    }
                    shift = from;
                    size = to - from;
                }

                public int size() {
                    return size;
                }

                public int get(int at) {
                    if (at < 0 || at >= size) {
                        throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
                    }
                    return IntList.this.get(at + shift);
                }

                public void addAt(int index, int value) {
                    throw new UnsupportedOperationException();
                }

                public void removeAt(int index) {
                    throw new UnsupportedOperationException();
                }

                public void set(int at, int value) {
                    if (at < 0 || at >= size) {
                        throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
                    }
                    IntList.this.set(at + shift, value);
                }

                public IntList compute() {
                    return new IntArrayList(this);
                }
            };
        }

    }

    static class IntArray extends IntAbstractStream implements IntList {
        private int[] data;

        public IntArray(int[] arr) {
            data = arr;
        }

        public int size() {
            return data.length;
        }

        public int get(int at) {
            return data[at];
        }

        public void addAt(int index, int value) {
            throw new UnsupportedOperationException();
        }

        public void removeAt(int index) {
            throw new UnsupportedOperationException();
        }

        public void set(int index, int value) {
            data[index] = value;
        }

    }

    static class Sorter {
        private static final int INSERTION_THRESHOLD = 16;

        private Sorter() {
        }

        public static void sort(IntList list, IntComparator comparator) {
            quickSort(list, 0, list.size() - 1, (Integer.bitCount(Integer.highestOneBit(list.size()) - 1) * 5) >> 1,
                    comparator);
        }

        private static void quickSort(IntList list, int from, int to, int remaining, IntComparator comparator) {
            if (to - from < INSERTION_THRESHOLD) {
                insertionSort(list, from, to, comparator);
                return;
            }
            if (remaining == 0) {
                heapSort(list, from, to, comparator);
                return;
            }
            remaining--;
            int pivotIndex = (from + to) >> 1;
            int pivot = list.get(pivotIndex);
            list.swap(pivotIndex, to);
            int storeIndex = from;
            int equalIndex = to;
            for (int i = from; i < equalIndex; i++) {
                int value = comparator.compare(list.get(i), pivot);
                if (value < 0) {
                    list.swap(storeIndex++, i);
                } else if (value == 0) {
                    list.swap(--equalIndex, i--);
                }
            }
            quickSort(list, from, storeIndex - 1, remaining, comparator);
            for (int i = equalIndex; i <= to; i++) {
                list.swap(storeIndex++, i);
            }
            quickSort(list, storeIndex, to, remaining, comparator);
        }

        private static void heapSort(IntList list, int from, int to, IntComparator comparator) {
            for (int i = (to + from - 1) >> 1; i >= from; i--) {
                siftDown(list, i, to, comparator, from);
            }
            for (int i = to; i > from; i--) {
                list.swap(from, i);
                siftDown(list, from, i - 1, comparator, from);
            }
        }

        private static void siftDown(IntList list, int start, int end, IntComparator comparator, int delta) {
            int value = list.get(start);
            while (true) {
                int child = ((start - delta) << 1) + 1 + delta;
                if (child > end) {
                    return;
                }
                int childValue = list.get(child);
                if (child + 1 <= end) {
                    int otherValue = list.get(child + 1);
                    if (comparator.compare(otherValue, childValue) > 0) {
                        child++;
                        childValue = otherValue;
                    }
                }
                if (comparator.compare(value, childValue) >= 0) {
                    return;
                }
                list.swap(start, child);
                start = child;
            }
        }

        private static void insertionSort(IntList list, int from, int to, IntComparator comparator) {
            for (int i = from + 1; i <= to; i++) {
                int value = list.get(i);
                for (int j = i - 1; j >= from; j--) {
                    if (comparator.compare(list.get(j), value) <= 0) {
                        break;
                    }
                    list.swap(j, j + 1);
                }
            }
        }

    }

    static interface IntTask {
        public void process(int value);

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public void readIntArrays(int[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readInt();
                }
            }
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine() {
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class ListIndependentSetSystem implements IndependentSetSystem {
        private final IntList[] lists;
        private int[] parent;
        private int setCount;
        private IndependentSetSystem.Listener listener;

        public ListIndependentSetSystem(int size) {
            lists = new IntList[size];
            parent = new int[size];
            for (int i = 0; i < size; i++) {
                parent[i] = i;
            }
            setCount = size;
        }

        public boolean join(int first, int second) {
            first = parent[first];
            second = parent[second];
            if (first == second) {
                return false;
            }
            int firstSize = lists[first] == null ? 1 : lists[first].size() + 1;
            int secondSize = lists[second] == null ? 1 : lists[second].size() + 1;
            if (firstSize < secondSize) {
                int temp = first;
                first = second;
                second = temp;
            }
            if (lists[first] == null) {
                lists[first] = new IntArrayList();
            }
            lists[first].add(second);
            parent[second] = first;
            if (lists[second] != null) {
                lists[first].addAll(lists[second]);
                final int finalFirst = first;
                lists[second].forEach((IntTask) i -> parent[i] = finalFirst);
            }
            lists[second] = null;
            if (listener != null) {
                listener.joined(second, first);
            }
            setCount--;
            return true;
        }

        public int get(int index) {
            return parent[index];
        }

        public int getSize(int vertex) {
            vertex = parent[vertex];
            if (lists[vertex] == null) {
                return 1;
            }
            return lists[vertex].size() + 1;
        }

    }

    static interface LongFilter {
        public boolean accept(long value);

    }

    static interface IntCollection extends IntStream {
        public int size();

        default public void add(int value) {
            throw new UnsupportedOperationException();
        }

        default public int[] toArray() {
            int size = size();
            int[] array = new int[size];
            int i = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                array[i++] = it.value();
            }
            return array;
        }

        default public IntCollection addAll(IntStream values) {
            for (IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
                add(it.value());
            }
            return this;
        }

    }

    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        IntIterator intIterator();

        default Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();

                public boolean hasNext() {
                    return it.isValid();
                }

                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }

        default int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if (i < j) {
                    return -1;
                } else if (i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if (it.isValid()) {
                return 1;
            }
            if (jt.isValid()) {
                return -1;
            }
            return 0;
        }

        default void forEach(IntTask task) {
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                task.process(it.value());
            }
        }

    }

    static class MiscUtils {
        public static long binarySearch(long from, long to, LongFilter function) {
            while (from < to) {
                long argument = from + ((to - from) >> 1);
                if (function.accept(argument)) {
                    to = argument;
                } else {
                    from = argument + 1;
                }
            }
            return from;
        }

        public static void decreaseByOne(int[]... arrays) {
            for (int[] array : arrays) {
                for (int i = 0; i < array.length; i++) {
                    array[i]--;
                }
            }
        }

    }

    static interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

    static class Range {
        public static IntList range(int from, int to) {
            int[] result = new int[Math.abs(from - to)];
            int current = from;
            if (from <= to) {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current++;
                }
            } else {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current--;
                }
            }
            return new IntArray(result);
        }

    }

    static class ArrayUtils {
        public static int[] range(int from, int to) {
            return Range.range(from, to).toArray();
        }

        public static int[] createOrder(int size) {
            return range(0, size);
        }

        public static int[] sort(int[] array, IntComparator comparator) {
            return sort(array, 0, array.length, comparator);
        }

        public static int[] sort(int[] array, int from, int to, IntComparator comparator) {
            if (from == 0 && to == array.length) {
                new IntArray(array).sort(comparator);
            } else {
                new IntArray(array).subList(from, to).sort(comparator);
            }
            return array;
        }

        public static int[] order(final int[] array) {
            return sort(createOrder(array.length), (first, second) -> Integer.compare(array[first], array[second]));
        }

        public static long[] partialSums(long[] array) {
            long[] result = new long[array.length + 1];
            for (int i = 0; i < array.length; i++) {
                result[i + 1] = result[i] + array[i];
            }
            return result;
        }

    }

    static interface IntReversableCollection extends IntCollection {
    }

    static abstract class IntAbstractStream implements IntStream {
        public String toString() {
            StringBuilder builder = new StringBuilder();
            boolean first = true;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                if (first) {
                    first = false;
                } else {
                    builder.append(' ');
                }
                builder.append(it.value());
            }
            return builder.toString();
        }

        public boolean equals(Object o) {
            if (!(o instanceof IntStream)) {
                return false;
            }
            IntStream c = (IntStream) o;
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                if (it.value() != jt.value()) {
                    return false;
                }
                it.advance();
                jt.advance();
            }
            return !it.isValid() && !jt.isValid();
        }

        public int hashCode() {
            int result = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                result *= 31;
                result += it.value();
            }
            return result;
        }

    }

    static class IntArrayList extends IntAbstractStream implements IntList {
        private int size;
        private int[] data;

        public IntArrayList() {
            this(3);
        }

        public IntArrayList(int capacity) {
            data = new int[capacity];
        }

        public IntArrayList(IntCollection c) {
            this(c.size());
            addAll(c);
        }

        public IntArrayList(IntStream c) {
            this();
            if (c instanceof IntCollection) {
                ensureCapacity(((IntCollection) c).size());
            }
            addAll(c);
        }

        public IntArrayList(IntArrayList c) {
            size = c.size();
            data = c.data.clone();
        }

        public IntArrayList(int[] arr) {
            size = arr.length;
            data = arr.clone();
        }

        public int size() {
            return size;
        }

        public int get(int at) {
            if (at >= size) {
                throw new IndexOutOfBoundsException("at = " + at + ", size = " + size);
            }
            return data[at];
        }

        private void ensureCapacity(int capacity) {
            if (data.length >= capacity) {
                return;
            }
            capacity = Math.max(2 * data.length, capacity);
            data = Arrays.copyOf(data, capacity);
        }

        public void addAt(int index, int value) {
            ensureCapacity(size + 1);
            if (index > size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size) {
                System.arraycopy(data, index, data, index + 1, size - index);
            }
            data[index] = value;
            size++;
        }

        public void removeAt(int index) {
            if (index >= size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size - 1) {
                System.arraycopy(data, index + 1, data, index, size - index - 1);
            }
            size--;
        }

        public void set(int index, int value) {
            if (index >= size) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            data[index] = value;
        }

        public int[] toArray() {
            return Arrays.copyOf(data, size);
        }

    }
}