Problem: Easy and hard versions are actually different problems, so we advise you to read both statements carefully.

You are given a weighted rooted tree, vertex 1 is the root of this tree.

A tree is a connected graph without cycles. A rooted tree has a special vertex called the root. A parent of a vertex v is the last different from v vertex on the path from the root to the vertex v. Children of vertex v are all vertices for which v is the parent. A vertex is a leaf if it has no children. The weighted tree is such a tree that each edge of this tree has some weight.

The weight of the path is the sum of edges weights on this path. The weight of the path from the vertex to itself is 0.

You can make a sequence of zero or more moves. On each move, you select an edge and divide its weight by 2 rounding down. More formally, during one move, you choose some edge i and divide its weight by 2 rounding down (w_i := \left⌊(w_i)/(2)\right⌋).

Your task is to find the minimum number of moves required to make the sum of weights of paths from the root to each leaf at most S. In other words, if w(i, j) is the weight of the path from the vertex i to the vertex j, then you have to make ∑_{v ∈ leaves} w(root, v) ≤ S, where leaves is the list of all leaves.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains two integers n and S (2 ≤ n ≤ 10^5; 1 ≤ S ≤ 10^{16}) — the number of vertices in the tree and the maximum possible sum of weights you have to obtain. The next n-1 lines describe edges of the tree. The edge i is described as three integers v_i, u_i and w_i (1 ≤ v_i, u_i ≤ n; 1 ≤ w_i ≤ 10^6), where v_i and u_i are vertices the edge i connects and w_i is the weight of this edge.

It is guaranteed that the sum of n does not exceed 10^5 (∑ n ≤ 10^5).

Output

For each test case, print the answer: the minimum number of moves required to make the sum of weights of paths from the root to each leaf at most S.

Example

Input


3
3 20
2 1 8
3 1 7
5 50
1 3 100
1 5 10
2 3 123
5 4 55
2 100
1 2 409


Output


0
8
3

Solution (in JAVA):

Solution:
//package start;

import java.io.*;
import java.lang.*;
import java.util.*;
import java.util.function.BiFunction;

public class Main extends IO {

    private static PriorityQueue<Pair<Integer, Long>> queue = new PriorityQueue<>(Comparator.comparingLong((value -> -((value.getSecondElement() - (value.getSecondElement() >> 1)) * value.getFirstElement()))));


    public static void main(String[] args) throws Exception {
        int count = readInt();
        for (int i = 0; i < count; i++) {
            long[] quantity = readArrayLong(" ");
            queue.clear();
            Graph graph = new Graph();
            graph.edgesMatrixToDefault((int) quantity[0], (int) quantity[0] - 1, true, null);
            graph.dfs(0, 0);
            long sum = 0;
            for (Pair<Integer, Long> value : queue) {
                sum += (value.getSecondElement() * value.getFirstElement());
            }
            long answer = 0;
            while (sum > quantity[1]) {
                Pair<Integer, Long> value = queue.poll();
                Long price = value.getSecondElement();
                sum -= (price - (price >>= 1)) * value.getFirstElement();
                value.setSecond(price);
                queue.add(value);
                answer++;
            }
            writeLong(answer, "\n");
        }

        print();
    }



    static void incEdges(long inc, int count) {
        queue.add(Pair.createPair(count, inc));
    }
}


class math {

    protected static int remains = 0x989687; // 10000007

    protected static int gcd(int a, int b) { // NOD
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

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

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

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

    protected static double lcm(double a, double b) { // NOK
        return a / gcd(a, b) * b;
    }

    protected static float lcm(float a, float b) { // NOK
        return a / gcd(a, b) * b;
    }

    protected static int lcm(int a, int b) { // NOK
        return a / gcd(a, b) * b;
    }

    protected static long lcm(long a, long b) {
        return a / gcd(a, b) * b;

    }

    protected static double log(double value, int base) {
        return Math.log(value) / Math.log(base);
    }

    protected static long factorial(int number) {
        if (number < 0) {
            return 0;
        }
        return solveFactorial(number);
    }

    private static long solveFactorial(int number) {
        if (number > 0) {
            return solveFactorial(number - 1) * number;
        }
        return 1;
    }

}

class Int implements Comparable<Integer> {

    protected int value;

    Int(int value) {
        this.value = value;
    }

    public Int add(int value) {
        this.value += value;
        return this;
    }

    @Override
    public int compareTo(Integer o) {
        return (this.value < o) ? -1 : ((this.value == o) ? 0 : 1);
    }

    @Override
    public boolean equals(Object obj) {
        if (obj instanceof Integer) {
            return value == (Integer) obj;
        }
        return false;
    }

    @Override
    public int hashCode() {
        return value;
    }

    @Override
    protected void finalize() throws Throwable {
        super.finalize();
    }
}


class Fraction<T extends Number> extends Pair {

    private Fraction(T dividend, T divider) {
        super(dividend, divider);
        reduce();
    }

    protected static <T extends Number> Fraction<T> createFraction(T dividend, T divider) {
        return new Fraction<>(dividend, divider);
    }

    protected void reduce() {
        if (getFirstElement() instanceof Integer) {
            Integer Dividend = (Integer) getFirstElement();
            Integer Divider = (Integer) getSecondElement();
            int gcd = math.gcd(Dividend, Divider);
            setFirst(Dividend / gcd);
            setSecond(Divider / gcd);
        } else if (getFirstElement() instanceof Long) {
            Long Dividend = (Long) getFirstElement();
            Long Divider = (Long) getSecondElement();
            long gcd = math.gcd(Dividend, Divider);
            setFirst(Dividend / gcd);
            setSecond(Divider / gcd);
        } else if (getFirstElement() instanceof Float) {
            Float Dividend = (Float) getFirstElement();
            Float Divider = (Float) getSecondElement();
            float gcd = math.gcd(Dividend, Divider);
            setFirst(Dividend / gcd);
            setSecond(Divider / gcd);
        } else if (getFirstElement() instanceof Double) {
            Double Dividend = (Double) getFirstElement();
            Double Divider = (Double) getSecondElement();
            double gcd = math.gcd(Dividend, Divider);
            setFirst(Dividend / gcd);
            setSecond(Divider / gcd);
        }
    }

    protected void addWithoutReturn(Fraction number) throws UnsupportedOperationException {
        add(number, 0);
    }

    private Fraction add(Fraction number, int function) throws UnsupportedOperationException {
        if (getFirstElement() instanceof Integer && number.getFirstElement() instanceof Integer) {
            Integer Dividend = (Integer) getFirstElement();
            Integer Divider = (Integer) getSecondElement();
            Integer Dividend1 = (Integer) number.getFirstElement();
            Integer Divider1 = (Integer) number.getSecondElement();
            Integer lcm = math.lcm(Divider, Divider1);
            if (function == 0) {
                setFirst((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1);
                setSecond(lcm);
                reduce();
                return null;
            }
            Fraction result = Fraction.createFraction((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1, lcm);
            result.reduce();
            return result;

        } else if (getFirstElement() instanceof Long && number.getFirstElement() instanceof Long) {
            Long Dividend = (Long) getFirstElement();
            Long Divider = (Long) getSecondElement();
            Long Dividend1 = (Long) number.getFirstElement();
            Long Divider1 = (Long) number.getSecondElement();
            Long lcm = math.lcm(Divider, Divider1);
            if (function == 0) {
                setFirst((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1);
                setSecond(lcm);
                reduce();
                return null;
            }
            Fraction result = Fraction.createFraction((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1, lcm);
            result.reduce();
            return result;
        } else if (getFirstElement() instanceof Float && number.getFirstElement() instanceof Float) {
            Float Dividend = (Float) getFirstElement();
            Float Divider = (Float) getSecondElement();
            Float Dividend1 = (Float) number.getFirstElement();
            Float Divider1 = (Float) number.getSecondElement();
            Float lcm = math.lcm(Divider, Divider1);
            if (function == 0) {
                setFirst((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1);
                setSecond(lcm);
                reduce();
                return null;
            }
            Fraction result = Fraction.createFraction((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1, lcm);
            result.reduce();
            return result;
        } else if (getFirstElement() instanceof Double && number.getFirstElement() instanceof Double) {
            Double Dividend = (Double) getFirstElement();
            Double Divider = (Double) getSecondElement();
            Double Dividend1 = (Double) number.getFirstElement();
            Double Divider1 = (Double) number.getSecondElement();
            Double lcm = math.lcm(Divider, Divider1);
            if (function == 0) {
                setFirst((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1);
                setSecond(lcm);
                reduce();
                return null;
            }
            Fraction result = Fraction.createFraction((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1, lcm);
            result.reduce();
            return result;
        } else {
            throw new UnsupportedOperationException();
        }
    }

    protected Fraction addWithReturn(Fraction number) {
        return add(number, 1);
    }

    protected void multiplyWithoutReturn(Fraction number) throws UnsupportedOperationException {
        multiply(number, 0);
    }

    protected Fraction multiplyWithReturn(Fraction number) throws UnsupportedOperationException {
        return multiply(number, 1);
    }

    private Fraction multiply(Fraction number, int function) throws UnsupportedOperationException {
        if (getFirstElement() instanceof Integer && number.getFirstElement() instanceof Integer) {
            Integer first = (Integer) getFirstElement() * (Integer) number.getFirstElement();
            Integer second = (Integer) getSecondElement() * (Integer) number.getSecondElement();
            if (function == 0) {
                setFirst(first);
                setSecond(second);
                reduce();
                return null;
            }
            Fraction answer = Fraction.createFraction(first, second);
            answer.reduce();
            return answer;
        } else if (getFirstElement() instanceof Long && number.getFirstElement() instanceof Long) {
            Long first = (Long) getFirstElement() * (Long) number.getFirstElement();
            Long second = (Long) getSecondElement() * (Long) number.getSecondElement();
            if (function == 0) {
                setFirst(first);
                setSecond(second);
                reduce();
                return null;
            }
            Fraction answer = Fraction.createFraction(first, second);
            answer.reduce();
            return answer;

        } else if (getFirstElement() instanceof Float && number.getFirstElement() instanceof Float) {
            Float first = (Float) getFirstElement() * (Float) number.getFirstElement();
            Float second = (Float) getSecondElement() * (Float) number.getSecondElement();
            if (function == 0) {
                setFirst(first);
                setSecond(second);
                reduce();
                return null;
            }
            Fraction answer = Fraction.createFraction(first, second);
            answer.reduce();
            return answer;
        } else if (getFirstElement() instanceof Double && number.getFirstElement() instanceof Double) {
            Double first = (Double) getFirstElement() * (Double) number.getFirstElement();
            Double second = (Double) getSecondElement() * (Double) number.getSecondElement();
            if (function == 0) {
                setFirst(first);
                setSecond(second);
                reduce();
                return null;
            }
            Fraction answer = Fraction.createFraction(first, second);
            answer.reduce();
            return answer;
        } else {
            throw new UnsupportedOperationException();
        }
    }
}

class Pair<T, T1> implements Cloneable {

    private T first;
    private T1 second;

    Pair(T obj, T1 obj1) {
        first = obj;
        second = obj1;
    }

    protected static <T, T1> Pair<T, T1> createPair(T element, T1 element1) {
        return new Pair<>(element, element1);
    }

    protected T getFirstElement() {
        return first;
    }

    protected T1 getSecondElement() {
        return second;
    }

    protected void setFirst(T element) {
        first = element;
    }

    protected void setSecond(T1 element) {
        second = element;
    }

    @Override
    public boolean equals(Object obj) {
        if (!(obj instanceof Pair)) {
            return false;
        }
        Pair pair = (Pair) obj;
        return first.equals(pair.first) && second.equals(pair.second);
    }

    @Override
    public int hashCode() {
        int hashCode = 1;
        hashCode = 31 * hashCode + (first == null ? 0 : first.hashCode());
        return 31 * hashCode + (second == null ? 0 : second.hashCode());
    }

    @Override
    public Object clone() {
        return Pair.createPair(first, second);
    }
}

class Graph {

    private int[][] base;
    private boolean[] used;
    private int quantity;
    private Integer[] ancestor;

    public int[][] getBase() {
        return base;
    }

    public boolean[] getUsed() {
        return used;
    }

    public int getQuantity() {
        return quantity;
    }

    public Integer[] getAncestor() {
        return ancestor;
    }

    public void setBase(int[][] base) {
        this.base = base;
    }

    protected void start(int length) {
        used = new boolean[length];
        ancestor = new Integer[length];
        Arrays.fill(ancestor, -1);
        quantity = 0;
    }


    protected void edgesMatrixToDefault(int length, int inputQuantity, boolean readConsole, int[][] value) throws Exception {
        base = new int[length][];
        List<ArrayList<Integer>> inputBase = new ArrayList<>();
        for (int i = 0; i < length; i++) {
            inputBase.add(new ArrayList<>());
        }
        for (int i = 0; i < inputQuantity; i++) {
            int[] input = readConsole ? IO.readArrayInt(" ") : value[i];
            inputBase.get(input[0] - 1).add(input[1] - 1);
            inputBase.get(input[0] - 1).add(input[2]); // price
            inputBase.get(input[1] - 1).add(input[0] - 1);
            inputBase.get(input[1] - 1).add(input[2]); // price
        }
        for (int i = 0; i < length; i++) {
            base[i] = inputBase.get(i).stream().mapToInt(Integer::intValue).toArray();
        }
        start(length);
    }

    protected void adjacencyMatrixToDefault(int length, int not, boolean readConsole, int[][] value) throws Exception {
        this.base = new int[length][];
        List<Integer> buffer = new ArrayList<>();
        for (int i = 0; i < length; i++) {
            int[] InputArray = readConsole ? IO.readArrayInt(" ") : value[i];
            for (int index = 0; index < length; index++) {
                if (i != index && InputArray[index] != not) {
                    buffer.add(index);
                    // buffer.add(InputArray[index]); // price
                }
            }
            this.base[i] = buffer.stream().mapToInt(Integer::intValue).toArray();
            buffer.clear();
        }
        start(length);
    }

    protected int dfs(int position, long price) throws Exception {
        used[position] = true;
        int next;
        int count = 0;
        for (int index = 0; index < base[position].length; index += 2) {
            next = base[position][index];
            if (!used[next]) {
                ancestor[next] = position;
                count += dfs(next, base[position][index + 1]);
            }
        }
        if (base[position].length == 2 && base[position][0] == ancestor[position]) {
            Main.incEdges(price, 1);
            return 1;
        } else if (position != 0) {
            Main.incEdges(price, count);
        }
        return count;
    }

    protected int dijkstra(int start, int stop, int size) {
        start--;
        stop--;
        int[] dist = new int[size];
        for (int i = 0; i < size; i++) {
            if (i != start) {
                dist[i] = Integer.MAX_VALUE;
            }
            ancestor[i] = start;
        }

        Queue<int[]> queue = new PriorityQueue<>(Comparator.comparingInt((int[] ints) -> ints[1]));
        queue.add(new int[]{start, 0});
        int position;
        int[] getQueue;
        while (queue.size() != 0) {
            getQueue = queue.poll();
            position = getQueue[0];
            if (getQueue[1] > dist[position]) {
                continue;
            }
            for (int index = 0; index < this.base[position].length; index += 2) {
                if (dist[position] + this.base[position][index + 1] < dist[this.base[position][index]] && !this.used[this.base[position][index]]) {
                    dist[this.base[position][index]] = dist[position] + this.base[position][index + 1];
                    this.ancestor[this.base[position][index]] = position;
                    queue.add(new int[]{this.base[position][index], dist[this.base[position][index]]});
                }
            }
            used[position] = true;
        }
        return dist[stop] == Integer.MAX_VALUE ? -1 : dist[stop];
    }

    protected static boolean solveFloydWarshall(int[][] base, int length, int not) {
        for (int k = 0; k < length; k++) {
            for (int i = 0; i < length; i++) {
                for (int j = 0; j < length; j++) {
                    if (base[i][k] == not || base[k][j] == not) {
                        continue;
                    }
                    int total = base[i][k] + base[k][j];
                    if (base[i][j] != not) {
                        base[i][j] = Math.min(base[i][j], total);
                    } else {
                        base[i][j] = total;
                    }
                }
            }
        }
        for (int index = 0; index < length; index++) {
            if (base[index][index] != 0) { // if cycle
                return false;
            }
        }
        return true;
    }

    protected static Pair<Long, int[][]> solveKruskal(int[][] edgesMatrix, final int countVertex, final int indexSort) {
        int[][] answer = new int[countVertex - 1][2];
        long sum = 0;
        Arrays.sort(edgesMatrix, Comparator.comparingInt(value -> value[indexSort]));
        SystemOfDisjointSets dsu = new SystemOfDisjointSets(countVertex);
        for (int i = 0; i < countVertex; i++) {
            dsu.makeSet(i);
        }
        int index = 0;
        for (int[] value : edgesMatrix) {
            if (dsu.mergeSets(value[0], value[1])) {
                sum += value[indexSort];
                answer[index] = new int[]{value[0], value[1]};
                index++;
            }
        }
        if (index < countVertex - 1) {
            return Pair.createPair(null, null);
        }
        return Pair.createPair(sum, answer);
    }

    static class SegmentTree {

        private int[] segmentArray;
        private BiFunction<Integer, Integer, Integer> function;

        protected void setSegmentArray(int[] segmentArray) {
            this.segmentArray = segmentArray;
        }

        protected int[] getSegmentArray() {
            return segmentArray.clone();
        }

        protected void setFunction(BiFunction<Integer, Integer, Integer> function) {
            this.function = function;
        }

        protected BiFunction<Integer, Integer, Integer> getFunction() {
            return function;
        }

        SegmentTree() {

        }

        SegmentTree(int[] startBase, int neutral, BiFunction<Integer, Integer, Integer> function) {
            this.function = function;
            int length = startBase.length;
            int[] base;
            if ((length & (length - 1)) != 0) {
                int pow = 0;
                while (length > 0) {
                    length >>= 1;
                    pow++;
                }
                pow--;
                base = new int[2 << pow];
                System.arraycopy(startBase, 0, base, 0, startBase.length);
                Arrays.fill(base, startBase.length, base.length, neutral);

            } else {
                base = startBase;
            }
            segmentArray = new int[base.length << 1]; // maybe * 4
            Arrays.fill(segmentArray, neutral);
            inDepth(base, 1, 0, base.length - 1);
        }

        private void inDepth(int[] base, int position, int low, int high) {
            if (low == high) {
                segmentArray[position] = base[low];
            } else {
                int mid = (low + high) >> 1;
                inDepth(base, position << 1, low, mid);
                inDepth(base, (position << 1) + 1, mid + 1, high);
                segmentArray[position] = function.apply(segmentArray[position << 1], segmentArray[(position << 1) + 1]);
            }
        }

        protected int getValue(int left, int right, int neutral) {
            return findValue(1, 0, ((segmentArray.length) >> 1) - 1, left, right, neutral);
        }

        private int findValue(int position, int low, int high, int left, int right, int neutral) {
            if (left > right) {
                return neutral;
            }
            if (left == low && right == high) {
                return segmentArray[position];
            }
            int mid = (low + high) >> 1;
            return function.apply(findValue(position << 1, low, mid, left, Math.min(right, mid), neutral),
                    findValue((position << 1) + 1, mid + 1, high, Math.max(left, mid + 1), right, neutral));
        }

        protected void replaceValue(int index, int value) {
            update(1, 0, (segmentArray.length >> 1) - 1, index, value);
        }

        private void update(int position, int low, int high, int index, int value) {
            if (low == high) {
                segmentArray[position] = value;
            } else {
                int mid = (low + high) >> 1;
                if (index <= mid) {
                    update(position << 1, low, mid, index, value);
                } else {
                    update((position << 1) + 1, mid + 1, high, index, value);
                }
                segmentArray[position] = function.apply(segmentArray[position << 1], segmentArray[(position << 1) + 1]);
            }
        }
    }

    static class SegmentTreeGeneric<T> {

        private Object[] segmentArray;
        private BiFunction<T, T, T> function;

        protected void setSegmentArray(T[] segmentArray) {
            this.segmentArray = segmentArray;
        }

        protected Object getSegmentArray() {
            return segmentArray.clone();
        }

        protected void setFunction(BiFunction<T, T, T> function) {
            this.function = function;
        }

        protected BiFunction<T, T, T> getFunction() {
            return function;
        }

        SegmentTreeGeneric() {

        }

        SegmentTreeGeneric(T[] startBase, T neutral, BiFunction<T, T, T> function) {
            this.function = function;
            int length = startBase.length;
            Object[] base;
            if ((length & (length - 1)) != 0) {
                int pow = 0;
                while (length > 0) {
                    length >>= 1;
                    pow++;
                }
                pow--;
                base = new Object[2 << pow];
                System.arraycopy(startBase, 0, base, 0, startBase.length);
                Arrays.fill(base, startBase.length, base.length, neutral);

            } else {
                base = startBase;
            }
            segmentArray = new Object[base.length << 1]; // maybe * 4
            Arrays.fill(segmentArray, neutral);
            inDepth(base, 1, 0, base.length - 1);
        }

        private void inDepth(Object[] base, int position, int low, int high) {
            if (low == high) {
                segmentArray[position] = base[low];
            } else {
                int mid = (low + high) >> 1;
                inDepth(base, position << 1, low, mid);
                inDepth(base, (position << 1) + 1, mid + 1, high);
                segmentArray[position] = function.apply((T) segmentArray[position << 1], (T) segmentArray[(position << 1) + 1]);
            }
        }

        protected T getValue(int left, int right, T neutral) {
            return findValue(1, 0, ((segmentArray.length) >> 1) - 1, left, right, neutral);
        }

        private T findValue(int position, int low, int high, int left, int right, T neutral) {
            if (left > right) {
                return neutral;
            }
            if (left == low && right == high) {
                return (T) segmentArray[position];
            }
            int mid = (low + high) >> 1;
            return function.apply(findValue(position << 1, low, mid, left, Math.min(right, mid), neutral),
                    findValue((position << 1) + 1, mid + 1, high, Math.max(left, mid + 1), right, neutral));
        }

        protected void replaceValue(int index, T value) {
            update(1, 0, (segmentArray.length >> 1) - 1, index, value);
        }

        private void update(int position, int low, int high, int index, T value) {
            if (low == high) {
                segmentArray[position] = value;
            } else {
                int mid = (low + high) >> 1;
                if (index <= mid) {
                    update(position << 1, low, mid, index, value);
                } else {
                    update((position << 1) + 1, mid + 1, high, index, value);
                }
                segmentArray[position] = function.apply((T) segmentArray[position << 1], (T) segmentArray[(position << 1) + 1]);
            }
        }
    }
}

class SystemOfDisjointSets {

    private int[] rank;
    private int[] ancestor;

    SystemOfDisjointSets(int size) {
        this.rank = new int[size];
        this.ancestor = new int[size];
    }

    protected void makeSet(int value) {
        ancestor[value] = value;
        rank[value] = 0;
    }

    protected int findSet(int value) {
        if (value == ancestor[value]) {
            return value;
        }
        return ancestor[value] = findSet(ancestor[value]);
    }

    protected boolean mergeSets(int first, int second) {
        first = findSet(first);
        second = findSet(second);
        if (first != second) {
            if (rank[first] < rank[second]) {
                int number = first;
                first = second;
                second = number;
            }
            ancestor[second] = first;
            if (rank[first] == rank[second]) {
                rank[first]++;
            }
            return true;
        }
        return false;
    }
}

interface Array {
    void useArray(int[] a);
}

interface Method {
    void use();
}

class FastSort {

    protected static int[] sort(int[] array, int ShellHeapMergeMyInsertionSort) {
        sort(array, ShellHeapMergeMyInsertionSort, array.length);
        return array;
    }

    protected static int[] sortClone(int[] array, int ShellHeapMergeMyInsertionSort) {
        int[] base = array.clone();
        sort(base, ShellHeapMergeMyInsertionSort, array.length);
        return base;
    }

    private static void sort(int[] array, int ShellHeapMergeMyInsertionSort, int length) {
        if (ShellHeapMergeMyInsertionSort < 0 || ShellHeapMergeMyInsertionSort > 4) {
            Random random = new Random();
            ShellHeapMergeMyInsertionSort = random.nextInt(4);
        }
        if (ShellHeapMergeMyInsertionSort == 0) {
            ShellSort(array);
        } else if (ShellHeapMergeMyInsertionSort == 1) {
            HeapSort(array);
        } else if (ShellHeapMergeMyInsertionSort == 2) {
            MergeSort(array, 0, length - 1);
        } else if (ShellHeapMergeMyInsertionSort == 3) {
            straightMergeSort(array, length);
        } else if (ShellHeapMergeMyInsertionSort == 4) {
            insertionSort(array);
        }
    }

    private static void straightMergeSort(int[] array, int size) {
        if (size == 0) {
            return;
        }
        int length = (size >> 1) + ((size % 2) == 0 ? 0 : 1);
        Integer[][] ZeroBuffer = new Integer[length + length % 2][2];
        Integer[][] FirstBuffer = new Integer[0][0];
        for (int index = 0; index < length; index++) {
            int ArrayIndex = index << 1;
            int NextArrayIndex = (index << 1) + 1;
            if (NextArrayIndex < size) {
                if (array[ArrayIndex] > array[NextArrayIndex]) {
                    ZeroBuffer[index][0] = array[NextArrayIndex];
                    ZeroBuffer[index][1] = array[ArrayIndex];
                } else {
                    ZeroBuffer[index][0] = array[ArrayIndex];
                    ZeroBuffer[index][1] = array[NextArrayIndex];
                }
            } else {
                ZeroBuffer[index][0] = array[ArrayIndex];
            }
        }
        boolean position = false;
        int pointer0, pointer, pointer1, number = 4, NewPointer, count;
        Integer[][] NewBuffer;
        Integer[][] OldBuffer;
        length = (size >> 2) + ((size % 4) == 0 ? 0 : 1);
        while (true) {
            pointer0 = 0;
            count = (number >> 1) - 1;
            if (!position) {
                FirstBuffer = new Integer[length + length % 2][number];
                NewBuffer = FirstBuffer;
                OldBuffer = ZeroBuffer;
            } else {
                ZeroBuffer = new Integer[length + length % 2][number];
                NewBuffer = ZeroBuffer;
                OldBuffer = FirstBuffer;
            }
            for (int i = 0; i < length; i++) {
                pointer = 0;
                pointer1 = 0;
                NewPointer = pointer0 + 1;
                if (length == 1) {
                    for (int g = 0; g < size; g++) {
                        if (pointer > count || OldBuffer[pointer0][pointer] == null) {
                            array[g] = OldBuffer[NewPointer][pointer1];
                            pointer1++;
                        } else if (pointer1 > count || OldBuffer[NewPointer][pointer1] == null) {
                            if (OldBuffer[pointer0][pointer] == null) {
                                continue;
                            }
                            array[g] = OldBuffer[pointer0][pointer];
                            pointer++;
                        } else if (OldBuffer[pointer0][pointer] >= OldBuffer[NewPointer][pointer1]) {
                            array[g] = OldBuffer[NewPointer][pointer1];
                            pointer1++;
                        } else {
                            array[g] = OldBuffer[pointer0][pointer];
                            pointer++;
                        }
                    }
                    return;
                }
                for (int g = 0; g < number; g++) {
                    if (pointer > count || OldBuffer[pointer0][pointer] == null) {
                        if (OldBuffer[NewPointer][pointer1] == null) {
                            continue;
                        }
                        NewBuffer[i][g] = OldBuffer[NewPointer][pointer1];
                        pointer1++;
                    } else if (pointer1 > count || OldBuffer[NewPointer][pointer1] == null) {
                        if (OldBuffer[pointer0][pointer] == null) {
                            continue;
                        }
                        NewBuffer[i][g] = OldBuffer[pointer0][pointer];
                        pointer++;
                    } else if (OldBuffer[pointer0][pointer] >= OldBuffer[NewPointer][pointer1]) {
                        NewBuffer[i][g] = OldBuffer[NewPointer][pointer1];
                        pointer1++;
                    } else {
                        NewBuffer[i][g] = OldBuffer[pointer0][pointer];
                        pointer++;
                    }
                }
                pointer0 += 2;
            }
            position = !position;
            length = (length >> 1) + length % 2;
            number <<= 1;
        }
    }

    private static void ShellSort(int[] array) {
        int j;
        for (int gap = (array.length >> 1); gap > 0; gap >>= 1) {
            for (int i = gap; i < array.length; i++) {
                int temp = array[i];
                for (j = i; j >= gap && array[j - gap] > temp; j -= gap) {
                    array[j] = array[j - gap];
                }
                array[j] = temp;
            }
        }
    }

    private static void HeapSort(int[] array) {
        for (int i = (array.length >> 1) - 1; i >= 0; i--)
            shiftDown(array, i, array.length);
        for (int i = array.length - 1; i > 0; i--) {
            swap(array, 0, i);
            shiftDown(array, 0, i);
        }
    }

    private static void shiftDown(int[] array, int i, int n) {
        int child;
        int tmp;
        for (tmp = array[i]; leftChild(i) < n; i = child) {
            child = leftChild(i);
            if (child != n - 1 && (array[child] < array[child + 1]))
                child++;
            if (tmp < array[child])
                array[i] = array[child];
            else
                break;
        }
        array[i] = tmp;
    }

    private static int leftChild(int i) {
        return (i << 1) + 1;
    }

    private static void swap(int[] array, int i, int j) {
        int temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }

    private static void MergeSort(int[] array, int low, int high) {
        if (low < high) {
            int mid = (low + high) >> 1;
            MergeSort(array, low, mid);
            MergeSort(array, mid + 1, high);
            merge(array, low, mid, high);
        }
    }

    private static void merge(int[] array, int low, int mid, int high) {
        int n = high - low + 1;
        int[] Temp = new int[n];
        int i = low, j = mid + 1;
        int k = 0;
        while (i <= mid || j <= high) {
            if (i > mid)
                Temp[k++] = array[j++];
            else if (j > high)
                Temp[k++] = array[i++];
            else if (array[i] < array[j])
                Temp[k++] = array[i++];
            else
                Temp[k++] = array[j++];
        }
        for (j = 0; j < n; j++)
            array[low + j] = Temp[j];
    }

    private static void insertionSort(int[] elements) {
        for (int i = 1; i < elements.length; i++) {
            int key = elements[i];
            int j = i - 1;
            while (j >= 0 && key < elements[j]) {
                elements[j + 1] = elements[j];
                j--;
            }
            elements[j + 1] = key;
        }
    }
}

class IO {

    private static BufferedReader read;
    private static boolean fileInput = false;
    private static BufferedWriter write;
    private static boolean fileOutput = false;

    public static void setFileInput(boolean fileInput) {
        IO.fileInput = fileInput;
    }

    public static void setFileOutput(boolean fileOutput) {
        IO.fileOutput = fileOutput;
    }

    private static void startInput() {
        try {
            read = new BufferedReader(fileInput ? new FileReader("input.txt") : new InputStreamReader(System.in));
        } catch (Exception error) {
        }
    }

    private static void startOutput() {
        try {
            write = new BufferedWriter(fileOutput ? new FileWriter("output.txt") : new OutputStreamWriter(System.out));
        } catch (Exception error) {
        }
    }

    protected static int readInt() throws Exception {
        if (read == null) {
            startInput();
        }
        return Integer.parseInt(read.readLine());
    }

    protected static long readLong() throws Exception {
        if (read == null) {
            startInput();
        }
        return Long.parseLong(read.readLine());
    }

    protected static String readString() throws Exception {
        if (read == null) {
            startInput();
        }
        return read.readLine();
    }

    protected static int[] readArrayInt(String split) throws Exception {
        if (read == null) {
            startInput();
        }
        return Arrays.stream(read.readLine().split(split)).mapToInt(Integer::parseInt).toArray();
    }

    protected static long[] readArrayLong(String split) throws Exception {
        if (read == null) {
            startInput();
        }
        return Arrays.stream(read.readLine().split(split)).mapToLong(Long::parseLong).toArray();
    }

    protected static String[] readArrayString(String split) throws Exception {
        if (read == null) {
            startInput();
        }
        return read.readLine().split(split);
    }

    protected static void writeArray(int[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Integer.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception error) {
        }
    }

    protected static void writeArray(Integer[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Integer.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception error) {
        }
    }

    protected static void writeArray(long[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Long.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception error) {
        }
    }

    protected static void writeArray(Long[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Long.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception error) {
        }
    }

    public static void writeArray(String[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(array[index]);
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception ignored) {
        }
    }

    protected static void writeArray(boolean[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Boolean.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception ignored) {
        }
    }

    protected static void writeInt(int number, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(Integer.toString(number));
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeInt(Integer number, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(Integer.toString(number));
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeLong(long number, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(Long.toString(number));
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeLong(Long number, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(Long.toString(number));
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeString(String word, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(word);
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeBoolean(boolean value, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(value ? "true" : "false");
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeBoolean(Boolean value, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(value ? "true" : "false");
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeChar(char word, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(word);
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeChar(Character word, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(word);
            write.write(end);
        } catch (Exception ignored) {
        }
    }


    protected static void writeEnter() {
        if (write == null) {
            startOutput();
        }
        try {
            write.newLine();
        } catch (Exception ignored) {
        }
    }

    protected static void print(boolean exit) throws Exception {
        if (exit) {
            print();
        } else {
            write.flush();
        }
    }

    protected static void print() throws Exception {
        if (write == null) {
            return;
        }
        write.flush();
        if (read != null) {
            read.close();
        }
        write.close();
    }
}