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:
//not my code
//https://codeforces.com/blog/entry/89000
 
import java.util.*;
import java.io.*;
 
public class Main {
	static InputReader scn = new InputReader(System.in);
	static OutputWriter out = new OutputWriter(System.out);
	public static void main(String[] args) {
		// Running Number Of TestCases (t)
		int t = scn.nextInt();
		// int t = 1;
		while(t-- > 0)
			solve();
		out.close();
	}
 
	public static void dummy(){
		// Dummy Code for Rough
		int n = scn.nextInt();
		out.println(n);
	}
	static boolean[] dp;
	public static void solve() {
		// Main Solution (AC)
		int n = scn.nextInt();
		int[] arr = scn.readArrays(n);
		if(n == 1){
			out.println(1);
			out.println(1);
			return;
		}
		int[] temp = new int[n];
		for(int i = 0; i < n; i++) temp[i] = arr[i];
		{
		    Random rand = new Random();
		    for(int i = 1; i < n; i++) {
		        int j = rand.nextInt(i);
		        int tmp = temp[j];
		        temp[j] = temp[i];
		        temp[i] = tmp;
		    }
		}
		Arrays.sort(temp);
		HashSet<Integer> set = new HashSet<>(n);
		long[] prefix = new long[n];
		long sum = 0;	
		for(int i = 0; i < n; i++){
			sum += temp[i];
			prefix[i] = sum;
		}
		set.add(temp[n-1]);
		// out.println("Prefix Arrays is " + Arrays.toString(prefix));
		for(int i = n - 2; i >= 0; i--){
			if(prefix[i] >= temp[i+1]) set.add(temp[i]);
			else break;
		}
		List<Integer> list = new ArrayList<>(n);
		for(int i = 0; i < n; i++){
			if(set.contains(arr[i])) list.add(i+1);
		}
		out.println(list.size());
		for(int i : list) out.print(i + " ");
		out.println();
	}
 
	public static HashMap<Integer, Integer> CountFrequencies(int[] arr) {
 
		HashMap<Integer, Integer> map = new HashMap<>();
 
		for (int i : arr) {
			if (map.containsKey(i))
				map.put(i, map.get(i) + 1);
			else
				map.put(i, 1);
		}
		return map;
	}
 
	public static HashMap<Integer, Integer> sortByValue(HashMap<Integer, Integer> hm) {
        List<Map.Entry<Integer, Integer> > list = new LinkedList<Map.Entry<Integer, Integer> >(hm.entrySet());
        Collections.sort(list, new Comparator<Map.Entry<Integer, Integer> >() { 
            public int compare(Map.Entry<Integer, Integer> o1,  
                               Map.Entry<Integer, Integer> o2){ 
                return (o1.getValue()).compareTo(o2.getValue()); 
            } 
        });
        HashMap<Integer, Integer> temp = new LinkedHashMap<Integer, Integer>(); 
        for (Map.Entry<Integer, Integer> aa : list) { 
            temp.put(aa.getKey(), aa.getValue()); 
        } 
        return temp; 
    } 
 
	public static void sortbyColumn(int[][] arr, int col) {
		Arrays.sort(arr, new Comparator<int[]>() {
			public int compare(final int[] entry1, final int[] entry2) {
				if (entry1[col] > entry2[col])
					return 1;
				else
					return -1;
			}
		});
	}
 
	public static HashSet<Long> primeFactors(long n, HashSet<Long> list, int d) {
		list.add(1L);
		list.add(n);
		for (long i = 2; i <= Math.sqrt(n); i += 1) {
			long a = i;
			if (n % a == 0) {
				list.add(a);
				if (n % (n / a) == 0)
					list.add(n / a);
			}
		}
		return list;
	}
 
	public static void ArraySort2D(int[][] arr, int xy) {
		// xy == 0, for sorting wrt X-Axis
		// xy == 1, for sorting wrt Y-Axis
		Arrays.sort(arr, Comparator.comparingDouble(o -> o[xy]));
	}
 	
 	public static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}
 
	public static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}
 	
 	public static int binarySearch(int arr[], int l, int r, int x) {
		if (r >= l) {
			int mid = l + (r - l) / 2;
			if (arr[mid] == x)
				return mid;
			if (arr[mid] > x)
				return binarySearch(arr, l, mid - 1, x);
			return binarySearch(arr, mid + 1, r, x);
		}
		return -1;
	}
 
	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int[] readArrays(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = scn.nextInt();
			}
			return a;
		}
 
		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 nextInt() {
			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 long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long 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 String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		public String next() {
			return nextLine();
		}
 
		public interface SpaceCharFilter {
			public 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(1);
				}
				writer.print(objects[i]);
			}
		}
 
		public void println(Object... objects) {
			print(objects);
			writer.println();
		}
 
		public void close() {
			writer.close();
		}
	}
 
}