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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
long long power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
const long long L = 1e7;
long long tree[L];
long long f = 0;
long long h, g;
long long mapvals[L];
long long mapvals1[L];
void func(long long ind) {
  long long left = 2 * ind;
  long long right = 2 * ind + 1;
  if (tree[left] == 0 && tree[right] == 0) {
    tree[ind] = 0;
  } else {
    if (tree[left] > tree[right]) {
      tree[ind] = tree[left];
      mapvals1[tree[ind]] = ind;
      func(left);
      if (tree[left] == 0 && tree[right] == 0) {
        mapvals[tree[ind]] = ind;
      } else if (tree[left] > tree[right]) {
        mapvals[tree[ind]] = mapvals[tree[left]];
      } else {
        mapvals[tree[ind]] = mapvals[tree[right]];
      }
    } else {
      tree[ind] = tree[right];
      mapvals1[tree[ind]] = ind;
      func(right);
      if (tree[left] == 0 && tree[right] == 0) {
        mapvals[tree[ind]] = ind;
      } else if (tree[left] > tree[right]) {
        mapvals[tree[ind]] = mapvals[tree[left]];
      } else {
        mapvals[tree[ind]] = mapvals[tree[right]];
      }
    }
  }
}
long long assign(long long ind) {
  long long left = 2 * ind;
  long long right = 2 * ind + 1;
  if (tree[left] == 0 && tree[right] == 0)
    return mapvals[tree[ind]] = ind;
  else {
    long long a = assign(left);
    long long b = assign(right);
    if (tree[left] > tree[right])
      mapvals[tree[ind]] = a;
    else
      mapvals[tree[ind]] = b;
  }
  return mapvals[tree[ind]];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    cin >> h >> g;
    long long end = (1 << h) - 1;
    vector<long long> vals;
    long long total = 0;
    for (long long i = 1; i <= end; i++) {
      tree[i] = 0;
      mapvals[i] = 0;
      tree[2 * i] = 0;
      tree[2 * i + 1] = 0;
    }
    for (long long i = 1; i <= end; i++) {
      cin >> tree[i];
      total += tree[i];
      vals.push_back(tree[i]);
      mapvals1[tree[i]] = i;
    }
    mapvals[tree[1]] = assign(1);
    sort(vals.begin(), vals.end());
    reverse(vals.begin(), vals.end());
    long long c = 0;
    long long req = (1 << h) - (1 << g);
    long long i = 0;
    long long allowed = (1 << g) - 1;
    vector<long long> ans;
    while (c < req) {
      long long index = mapvals1[vals[i]];
      long long ch_index = mapvals[vals[i]];
      if (ch_index > allowed) {
        total -= vals[i];
        func(index);
        ans.push_back(index);
        c++;
      }
      i++;
    }
    cout << total << '\n';
    for (long long i = 0; i < (long long)(ans.size()); i++) {
      cout << ans[i] << ' ';
    }
    cout << '\n';
  }
  return 0;
}