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.util.*;import java.io.*;import java.math.*;
public class AccidentalVictory
{
    static final Random random=new Random();
    
    static void ruffleSort(int[] a) {
        int n = a.length; 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        ArrayList<Integer> lst = new ArrayList<>();
        for(int i : a)
            lst.add(i);
        Collections.sort(lst);
        for(int i = 0; i < n; i++)
            a[i] = lst.get(i);
    }

    static void ruffleSort(long[] a) {
        int n = a.length; 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        ArrayList<Long> lst = new ArrayList<>();
        for(long i : a)
            lst.add(i);
        Collections.sort(lst);
        for(int i = 0; i < n; i++)
            a[i] = lst.get(i);
    }

    public static void process()throws IOException
    {
        int n = ni();
        long[] a = nal(n);
        long[] pref = new long[n];
        if(n == 1){
            pn(1);
            pn(1);
            return;
        }
        ArrayList<Vict> ls = new ArrayList<>();
        for(int i = 0; i < n; i++)
            ls.add(new Vict(a[i], i+1));
        Collections.sort(ls, new Comparator<Vict>(){
            public int compare(Vict first, Vict second){
                return (int)(first.x - second.x);
            }
        });
        pref[0] = ls.get(0).x;
        for(int i = 1; i < n; i++)
            pref[i] = pref[i-1] + ls.get(i).x;
        long ans = 1;
        TreeSet<Long> st = new TreeSet<>();
        st.add(ls.get(n-1).y);
        int f = 0;
        for(int i = n-2; i > 0; i--){
            if(pref[i] >= ls.get(i+1).x){
                ans++;
                st.add(ls.get(i).y);
            }
            else{
                f = 1;
                break;
            }
        }
        if(f == 0){
            if(ls.get(0).x == ls.get(1).x){
                ans++;
                st.add(ls.get(0).y);
            }
        }
        pn(ans);
        for(long l : st)
            p(l+" ");
        pn("");
    }

    static class Vict{
        long x, y;
        Vict(long a, long b){
            x = a;
            y = b;
        }
    }
   
    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
        if(oj){sc=new AnotherReader();out=new PrintWriter(System.out);}
        else{sc=new AnotherReader(100);out=new PrintWriter("output.txt");}
        long s = System.currentTimeMillis();
        int t=1;
        t=ni();
        //int k = t;
        while(t-->0) {/*p("Case #"+ (k-t) + ": ")*/;process();}
        out.flush();
        System.err.println(System.currentTimeMillis()-s+"ms");
        out.close();
    }

    static long power(long k, long c, long mod){
        long y = 1;
        while(c > 0){
            if(c%2 == 1)
                y = y * k % mod;
            c = c/2;
            k = k * k % mod;
        }
        return y;
    }

 
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static int[] nai(int N)throws IOException{int[]A=new int[N];for(int i=0;i!=N;i++){A[i]=ni();}return A;}
    static long[] nal(int N)throws IOException{long[]A=new long[N];for(int i=0;i!=N;i++){A[i]=nl();}return A;}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////
 
    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}

/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}