Problem: A championship is held in Berland, in which n players participate. The player with the number i has a_i (a_i ≥ 1) tokens.

The championship consists of n-1 games, which are played according to the following rules:

  * in each game, two random players with non-zero tokens are selected; 
  * the player with more tokens is considered the winner of the game (in case of a tie, the winner is chosen randomly); 
  * the winning player takes all of the loser's tokens; 



The last player with non-zero tokens is the winner of the championship.

All random decisions that are made during the championship are made equally probable and independently.

For example, if n=4, a = [1, 2, 4, 3], then one of the options for the game (there could be other options) is: 

  * during the first game, the first and fourth players were selected. The fourth player has more tokens, so he takes the first player's tokens. Now a = [0, 2, 4, 4]; 
  * during the second game, the fourth and third players were selected. They have the same number of tokens, but in a random way, the third player is the winner. Now a = [0, 2, 8, 0]; 
  * during the third game, the second and third players were selected. The third player has more tokens, so he takes the second player's tokens. Now a = [0, 0, 10, 0]; 
  * the third player is declared the winner of the championship. 



Championship winners will receive personalized prizes. Therefore, the judges want to know in advance which players have a chance of winning, i.e have a non-zero probability of winning the championship. You have been asked to find all such players. 

Input

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

The first line of each test case consists of one positive integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of players in the championship.

The second line of each test case contains n positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the number of tokens the players have.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5. 

Output

For each test case, print the number of players who have a nonzero probability of winning the championship. On the next line print the numbers of these players in increasing order. Players are numbered starting from one in the order in which they appear in the input. 

Example

Input


2
4
1 2 4 3
5
1 1 1 1 1


Output


3
2 3 4 
5
1 2 3 4 5 

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.stream.*;
import java.lang.management.*;
import static java.lang.Math.*;

@SuppressWarnings("unchecked")
public class P1490E {

  public void run() throws Exception {
    Map<Integer, List<Integer>> ailm = new HashMap<>();

    for (int t = nextInt(); t > 0; t--) {
      ailm.clear();

      long sa = 0;
      Set<Integer> ans = new HashSet<>();

      for (int i = 1, n = nextInt(); i <= n; i++) {
        int a = nextInt();
        ans.add(i);
        sa += a;
        List<Integer> il = ailm.get(a);
        if (il == null) { il = new ArrayList<>(); ailm.put(a, il); }
        il.add(i);
      }

      List<Map.Entry<Integer, List<Integer>>> el = new ArrayList(ailm.entrySet());
      el.sort((a, b) -> a.getKey() - b.getKey());

      for (int i = el.size() - 1; i >= 0; i--) {
        Map.Entry<Integer, List<Integer>> me = el.remove(el.size() - 1);
        sa -= ((long)me.getKey()) * me.getValue().size();

        if (me.getKey() > sa) {
          break;
        }
      }

      for (Map.Entry<Integer, List<Integer>> me : el) {
        ans.removeAll(me.getValue());
      }

      println(ans.size());
      for (int i : new TreeSet<>(ans)) { print(i + " "); }
      println();
    }
  }

  public static void main(String... args) throws Exception {
    br = new BufferedReader(new InputStreamReader(System.in));
    pw = new PrintWriter(new BufferedOutputStream(System.out));
    new P1490E().run();
    br.close();
    pw.close();
    System.err.println("\n[Time : " + (System.currentTimeMillis() - startTime) + " ms]");
    long gct = 0, gcc = 0;
    for (GarbageCollectorMXBean garbageCollectorMXBean : ManagementFactory.getGarbageCollectorMXBeans()) {
      gct += garbageCollectorMXBean.getCollectionTime();
      gcc += garbageCollectorMXBean.getCollectionCount();
    }
    System.err.println("[GC time : " + gct + " ms, count = " + gcc + "]");
    System.err.println("[JIT time : " + ManagementFactory.getCompilationMXBean().getTotalCompilationTime() + " ms]");
  }

  static long startTime = System.currentTimeMillis();
  static BufferedReader br;
  static PrintWriter pw;
  StringTokenizer stok;

  String nextToken() throws IOException {
    while (stok == null || !stok.hasMoreTokens()) {
      String s = br.readLine();
      if (s == null) { return null; }
      stok = new StringTokenizer(s);
    }
    return stok.nextToken();
  }

  void print(byte b) { print("" + b); }
  void print(int i) { print("" + i); }
  void print(long l) { print("" + l); }
  void print(double d) { print("" + d); }
  void print(char c) { print("" + c); }
  void print(Object o) {
    if (o instanceof int[]) { print(Arrays.toString((int [])o));
    } else if (o instanceof long[]) { print(Arrays.toString((long [])o));
    } else if (o instanceof char[]) { print(Arrays.toString((char [])o));
    } else if (o instanceof byte[]) { print(Arrays.toString((byte [])o));
    } else if (o instanceof short[]) { print(Arrays.toString((short [])o));
    } else if (o instanceof boolean[]) { print(Arrays.toString((boolean [])o));
    } else if (o instanceof float[]) { print(Arrays.toString((float [])o));
    } else if (o instanceof double[]) { print(Arrays.toString((double [])o));
    } else if (o instanceof Object[]) { print(Arrays.toString((Object [])o));
    } else { print("" + o); }
  }
  void printsp(int [] a) { for (int i = 0, n = a.length; i < n; print(a[i] + " "), i++); }
  void printsp(long [] a) { for (int i = 0, n = a.length; i < n; print(a[i] + " "), i++); }
  void print(String s) { pw.print(s); }
  void println() { println(""); }
  void println(byte b) { println("" + b); }
  void println(int i) { println("" + i); }
  void println(long l) { println("" + l); }
  void println(double d) { println("" + d); }
  void println(char c) { println("" + c); }
  void println(Object o) { print(o); println(); }
  void println(String s) { pw.println(s); }
  int nextInt() throws IOException { return Integer.parseInt(nextToken()); }
  long nextLong() throws IOException { return Long.parseLong(nextToken()); }
  double nextDouble() throws IOException { return Double.parseDouble(nextToken()); }
  char nextChar() throws IOException { return (char) (br.read()); }
  String next() throws IOException { return nextToken(); }
  String nextLine() throws IOException { return br.readLine(); }
  int [] readInt(int size) throws IOException {
    int [] array = new int [size];
    for (int i = 0; i < size; i++) { array[i] = nextInt(); }
    return array;
  }
  long [] readLong(int size) throws IOException {
    long [] array = new long [size];
    for (int i = 0; i < size; i++) { array[i] = nextLong(); }
    return array;
  }
  double [] readDouble(int size) throws IOException {
    double [] array = new double [size];
    for (int i = 0; i < size; i++) { array[i] = nextDouble(); }
    return array;
  }
  String [] readLines(int size) throws IOException {
    String [] array = new String [size];
    for (int i = 0; i < size; i++) { array[i] = nextLine(); }
    return array;
  }

  int gcd(int a, int b) {
    if (a == 0) return Math.abs(b); if (b == 0) return Math.abs(a);
    a = Math.abs(a); b = Math.abs(b);
    int az = Integer.numberOfTrailingZeros(a), bz = Integer.numberOfTrailingZeros(b);
    a >>>= az; b >>>= bz;
    while (a != b) {
      if (a > b) { a -= b; a >>>= Integer.numberOfTrailingZeros(a); }
            else { b -= a; b >>>= Integer.numberOfTrailingZeros(b); }
    }
    return (a << Math.min(az, bz));
  }

  long gcd(long a, long b) {
    if (a == 0) return Math.abs(b); if (b == 0) return Math.abs(a);
    a = Math.abs(a); b = Math.abs(b);
    int az = Long.numberOfTrailingZeros(a), bz = Long.numberOfTrailingZeros(b);
    a >>>= az; b >>>= bz;
    while (a != b) {
      if (a > b) { a -= b; a >>>= Long.numberOfTrailingZeros(a); }
            else { b -= a; b >>>= Long.numberOfTrailingZeros(b); }
    }
    return (a << Math.min(az, bz));
  }

  boolean isPrime(int v) {
    if (v <= 1) { return false; }
    if (v <= 3) { return true; }
    if (((v & 1) == 0) || ((v % 3) == 0)) { return false; }
    for (int m = 5, n = (int)sqrt(v); m <= n; m += 6) { if (((v % m) == 0) || ((v % (m + 2)) == 0)) { return false; } }
    return true;
  }

  int [] rshuffle(int [] a) { // RANDOM shuffle
    Random r = new Random();
    for (int i = a.length - 1, j, t; i >= 0; j = r.nextInt(a.length), t = a[i], a[i] = a[j], a[j] = t, i--);
    return a;
  }

  int [] qshuffle(int [] a) { // QUICK shuffle
    int m = new Random().nextInt(10) + 2;
    for (int i = 0, n = a.length, j = m % n, t; i < n; t = a[i], a[i] = a[j], a[j] = t, i++, j = (i * m) % n);
    return a;
  }

  long [] shuffle(long [] a) {
    Random r = new Random();
    for (int i = a.length - 1; i >= 0; i--) {
      int j = r.nextInt(a.length);
      long t = a[i]; a[i] = a[j]; a[j] = t;
    }
    return a;
  }

  void shuffle(Object [] a) {
    Random r = new Random();
    for (int i = a.length - 1; i >= 0; i--) {
      int j = r.nextInt(a.length);
      Object t = a[i]; a[i] = a[j]; a[j] = t;
    }
  }

  int [] sort(int [] a) {
    final int SHIFT = 16, MASK = (1 << SHIFT) - 1, SIZE = (1 << SHIFT) + 1;
    int n = a.length, ta [] = new int [n], ai [] = new int [SIZE];
    for (int i = 0; i < n; ai[(a[i] & MASK) + 1]++, i++);
    for (int i = 1; i < SIZE; ai[i] += ai[i - 1], i++);
    for (int i = 0; i < n; ta[ai[a[i] & MASK]++] = a[i], i++);
    int [] t = a; a = ta; ta = t;
    ai = new int [SIZE];
    for (int i = 0; i < n; ai[(a[i] >> SHIFT) + 1]++, i++);
    for (int i = 1; i < SIZE; ai[i] += ai[i - 1], i++);
    for (int i = 0; i < n; ta[ai[a[i] >> SHIFT]++] = a[i], i++);
    return ta;
  }

  boolean nextPerm(int [] a) {
    int j, i = a.length - 2;
    for (; (i >= 0) && (a[i] > a[i + 1]); i--);
    if (i >= 0) {
      for (j = a.length - 1; a[i] > a[j]; j--);
      a[i] ^= a[j]; a[j] ^= a[i]; a[i] ^= a[j]; // swap(a[i], a[j])
      for (int l = i + 1, r = a.length - 1; l < r; l++, r--) {
        a[l] ^= a[r]; a[r] ^= a[l]; a[l] ^= a[r]; // swap(a[r], a[l])
      }
    }
    return (i >= 0);
  }

  void flush() {
    pw.flush();
  }

  void pause() {
    flush(); System.console().readLine();
  }
}