Problem: Drazil likes heap very much. So he created a problem with heap:

There is a max heap with a height h implemented on the array. The details of this heap are the following:

This heap contains exactly 2^h - 1 distinct positive non-zero integers. All integers are distinct. These numbers are stored in the array a indexed from 1 to 2^h-1. For any 1 < i < 2^h, a[i] < a[\left ⌊{i/2}\right ⌋].

Now we want to reduce the height of this heap such that the height becomes g with exactly 2^g-1 numbers in heap. To reduce the height, we should perform the following action 2^h-2^g times:

Choose an index i, which contains an element and call the following function f in index i:

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Note that we suppose that if a[i]=0, then index i don't contain an element.

After all operations, the remaining 2^g-1 element must be located in indices from 1 to 2^g-1. Now Drazil wonders what's the minimum possible sum of the remaining 2^g-1 elements. Please find this sum and find a sequence of the function calls to achieve this value.

Input

The first line of the input contains an integer t (1 ≤ t ≤ 70 000): the number of test cases.

Each test case contain two lines. The first line contains two integers h and g (1 ≤ g < h ≤ 20). The second line contains n = 2^h-1 distinct positive integers a[1], a[2], …, a[n] (1 ≤ a[i] < 2^{20}). For all i from 2 to 2^h - 1, a[i] < a[\left ⌊{i/2}\right ⌋].

The total sum of n is less than 2^{20}.

Output

For each test case, print two lines.

The first line should contain one integer denoting the minimum sum after reducing the height of heap to g. The second line should contain 2^h - 2^g integers v_1, v_2, …, v_{2^h-2^g}. In i-th operation f(v_i) should be called.

Example

Input


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


Output


10
3 2 3 1
8
2 1 3 1

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.Math;
import java.util.*;

public class Main  {

    public BufferedReader in;
    public PrintStream out;

    public boolean log_enabled = false;
    
    public boolean multiply_tests = true;

    public static boolean do_gen_test = false;
    
    public void gen_test() {
            
        
    }
    
    private class TestCase {

        int h;
        int g;

        long[] A;
                
        int N = 1, G = 1;
        
        public boolean can_delete(int v)
        {
            if (v>=G)
            {
                return true;
            }
            
            if ((A[2*v]==0)&&(A[2*v+1]==0))
            {
                return false;
            }
            
            if (A[2*v] > A[2*v+1])
            {
                return can_delete(2*v);
            }
            else
            {
                return can_delete(2*v+1);
            }
        }
        
        public void do_delete(int v)
        {
            if ((A[2*v]==0)&&(A[2*v+1]==0))
            {
                A[v] = 0;
                return;
            }
            
            if (A[2*v] > A[2*v+1])
            {
                A[v] = A[2*v];
                do_delete(2*v);
            }
            else
            {
                A[v] = A[2*v+1];
                do_delete(2*v+1);
            }
        }
        
        int[] D;
        int idx;
        
        public void select_delete(int v)
        {
            while (can_delete(v))
            {
                D[idx++] = v;
                do_delete(v);
            }
            
            if (A[2*v]>0)
            {
                select_delete(2*v);
            }
            
            if (A[2*v+1]>0)
            {
                select_delete(2*v+1);
            }
        }
        
        public Object solve() {
            
            h = readInt();
            g = readInt();
            
            
            int i;
            
            
            
            for (i=0; i<h; i++)
            {
                N = 2*N;
            }
            
            for (i=0; i<g; i++)
            {
                G = 2*G;
            }
            
            
            
            A = new long[2*N];
            for (i=1; i<N; i++)
            {
                A[i] = readLong();
            }
            
            for (i=N; i<2*N; i++)
            {
                A[i] = 0;
            }
            
            D = new int[N-G];
            
            select_delete(1);
            
            long S = 0;
            for (i=1; i<G; i++)
            {
                S += A[i];
            }
            
                        
            out.println(S);
            printArray(D, idx);
            
            
            return null;
            
            //return strf("%f", 0);
            
            //out.printf("Case #%d: \n", caseNumber);
            //return null;
        }
        
        public int caseNumber;
        
        TestCase(int number) {
            caseNumber = number;
        }
        
        public void run(){
            Object r = this.solve();
            
            if ((r != null))
            {
                //outputCaseNumber(r);
                out.println(r);
            }
        }
        
        public String impossible(){
            return "IMPOSSIBLE";
        }
        
        public String strf(String format, Object... args)
        {
            return String.format(format, args);
        }
        
//        public void outputCaseNumber(Object r){
//            //out.printf("Case #%d:", caseNumber);
//            if (r != null)
//            {
//              //  out.print(" ");
//                out.print(r);
//            }
//            out.print("\n");
//        }
    }

    public void run() {
        //while (true)
        {
            int t = multiply_tests ?  readInt() : 1;
            for (int i = 0; i < t; i++) {
                TestCase T = new TestCase(i + 1);
                T.run();
            }
        }
    }
    

    
    public Main(BufferedReader _in, PrintStream _out){
        in = _in;
        out = _out;
    }
    

    public static void main(String args[]) {
        Locale.setDefault(Locale.US);
        Main S;
        try {
            S = new Main(
                        new BufferedReader(new InputStreamReader(System.in)),
                        System.out
                );
        } catch (Exception e) {
            return;
        }
        
        S.run();
        
    }

    private StringTokenizer tokenizer = null;

    public int readInt() {
        return Integer.parseInt(readToken());
    }

    public long readLong() {
        return Long.parseLong(readToken());
    }

    public double readDouble() {
        return Double.parseDouble(readToken());
    }

    public String readLn() {
        try {
            String s;
            while ((s = in.readLine()).length() == 0);
            return s;
        } catch (Exception e) {
            return "";
        }
    }

    public String readToken() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(in.readLine());
            }
            return tokenizer.nextToken();
        } catch (Exception e) {
            return "";
        }
    }

    public int[] readIntArray(int n) {
        int[] x = new int[n];
        readIntArray(x, n);
        return x;
    }
    
    public int[] readIntArrayBuf(int n) {
        int[] x = new int[n];
        readIntArrayBuf(x, n);
        return x;
    }

    public void readIntArray(int[] x, int n) {
        for (int i = 0; i < n; i++) {
            x[i] = readInt();
        }
    }
    
    public long[] readLongArray(int n) {
        long[] x = new long[n];
        readLongArray(x, n);
        return x;
    }
    
    public long[] readLongArrayBuf(int n) {
        long[] x = new long[n];
        readLongArrayBuf(x, n);
        return x;
    }

    public void readLongArray(long[] x, int n) {
        for (int i = 0; i < n; i++) {
            x[i] = readLong();
        }
    }

    public void logWrite(String format, Object... args) {
        if (!log_enabled) {
            return;
        }

        out.printf(format, args);
    }
    
    public void readLongArrayBuf(long[] x, int n) {
        
        char[]buf = new char[1000000];
        long r = -1;
        int k= 0, l = 0;
        long d;
        
        while (true)
        {
            try{
                l = in.read(buf, 0, 1000000);
            }
            catch(Exception E){};
            
            for (int i=0; i<l; i++)
            {
                if (('0'<=buf[i])&&(buf[i]<='9'))
                {
                    if (r == -1)
                    {
                        r = 0;
                    }
                    d = buf[i] - '0';
                    r = 10 * r + d;
                }
                else
                {
                    if (r != -1)
                    {
                        x[k++] = r;
                    }
                    
                    r = -1;
                }
            }
            
            if (l<1000000)
                return;
        }
    }
    
    public void readIntArrayBuf(int[] x, int n) {
        
        char[]buf = new char[1000000];
        int r = -1;
        int k= 0, l = 0;
        int d;
        
        while (true)
        {
            try{
                l = in.read(buf, 0, 1000000);
            }
            catch(Exception E){};
            
            for (int i=0; i<l; i++)
            {
                if (('0'<=buf[i])&&(buf[i]<='9'))
                {
                    if (r == -1)
                    {
                        r = 0;
                    }
                    d = buf[i] - '0';
                    r = 10 * r + d;
                }
                else
                {
                    if (r != -1)
                    {
                        x[k++] = r;
                    }
                    
                    r = -1;
                }
            }
            
            if (l<1000000)
                return;
        }
    }
    
    public void printArray(long[] a, int n)
    {
        printArray(a, n, ' ');
    }
    
    public void printArray(int[] a, int n)
    {
        printArray(a, n, ' ');
    }
            
    public void printArray(long[] a, int n, char dl)
    {
        long x; 
        int i, l = 0;
        for (i=0; i<n; i++)
        {
            x = a[i];
            
            if (x<0)
            {
                x = -x;
                l++;
            }
            
            if (x==0)
            {
                l++;
            }
            else
            {
                while (x>0)
                {
                    x /= 10;
                    l++;
                }
            }
        }
        
        l += n-1;
        
        char[] s = new char[l];
        
        l--;
        boolean z;
        for (i=n-1; i>=0;  i--)
        {
            x = a[i];
            z = false;            
            if (x<0)
            {
                x = -x;
                z = true;
            }
            
            do{
                s[l--] = (char)('0' + (x % 10));
                x /= 10;
            } while (x>0);
            
            if (z)
            {
                s[l--] = '-';
            }
            
            if (i>0)
            {
                s[l--] = dl;
            }
        }
        
        out.println(new String(s));
    }
    
    public void printArray(int[] a, int n, char dl)
    {
        int x; 
        int i, l = 0;
        for (i=0; i<n; i++)
        {
            x = a[i];
            
            if (x<0)
            {
                x = -x;
                l++;
            }
            
            if (x==0)
            {
                l++;
            }
            else
            {
                while (x>0)
                {
                    x /= 10;
                    l++;
                }
            }
        }
        
        l += n-1;
        
        char[] s = new char[l];
        
        l--;
        boolean z;
        for (i=n-1; i>=0;  i--)
        {
            x = a[i];
            z = false;            
            if (x<0)
            {
                x = -x;
                z = true;
            }
            
            do{
                s[l--] = (char)('0' + (x % 10));
                x /= 10;
            } while (x>0);
            
            if (z)
            {
                s[l--] = '-';
            }
            
            if (i>0)
            {
                s[l--] = dl;
            }
        }
        
        out.println(new String(s));
    }
    
    public void printMatrix(int[][] a, int n, int m)
    {
        int x; 
        int i,j, l = 0;
        for (i=0; i<n; i++)
        {
            for (j=0; j<m; j++)
            {
                x = a[i][j];
            
                if (x<0)
                {
                    x = -x;
                    l++;
                }

                if (x==0)
                {
                    l++;
                }
                else
                {
                    while (x>0)
                    {
                        x /= 10;
                        l++;
                    }
                }
            }
            
            l += m-1;
        }
        
        l += n-1;
        
        
        char[] s = new char[l];
        
        l--;
        boolean z;
        for (i=n-1; i>=0;  i--)
        {
            for (j=m-1; j>=0;  j--)
            {
                x = a[i][j];
                z = false;            
                if (x<0)
                {
                    x = -x;
                    z = true;
                }

                do{
                    s[l--] = (char)('0' + (x % 10));
                    x /= 10;
                } while (x>0);

                if (z)
                {
                    s[l--] = '-';
                }

                if (j>0)
                {
                    s[l--] = ' ';
                }
            }
            
            if (i>0)
            {
                 s[l--] = '\n';
            }
        }
        
        out.println(new String(s));
    }
    
    public void printMatrix(long[][] a, int n, int m)
    {
        long x; 
        int i,j, l = 0;
        for (i=0; i<n; i++)
        {
            for (j=0; j<m; j++)
            {
                x = a[i][j];
            
                if (x<0)
                {
                    x = -x;
                    l++;
                }

                if (x==0)
                {
                    l++;
                }
                else
                {
                    while (x>0)
                    {
                        x /= 10;
                        l++;
                    }
                }
            }
            
            l += m-1;
        }
        
        l += n-1;
        
        
        char[] s = new char[l];
        
        l--;
        boolean z;
        for (i=n-1; i>=0;  i--)
        {
            for (j=m-1; j>=0;  j--)
            {
                x = a[i][j];
                z = false;            
                if (x<0)
                {
                    x = -x;
                    z = true;
                }

                do{
                    s[l--] = (char)('0' + (x % 10));
                    x /= 10;
                } while (x>0);

                if (z)
                {
                    s[l--] = '-';
                }

                if (j>0)
                {
                    s[l--] = ' ';
                }
            }
            
            if (i>0)
            {
                 s[l--] = '\n';
            }
        }
        
        out.println(new String(s));
    }
    
    
}