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 Task{
        //  ..............code begins here.............. 

static long mod=(long)1e9+7,inf=(long)1e15;
static int f(int[] a, int[] b){
    if(a[0]==b[0]) return a[1]-b[1];
    return a[0]-b[0];
}
static void solve() throws IOException {
        int n=int_v(read());
        int[] a=int_arr();
        int[][] b=new int[n][2];
        TreeSet<int[]> ts=new TreeSet<>((x,y)->f(x,y));
        for(int i=0;i<n;i++){
            b[i][0]=a[i];b[i][1]=i;
        }
        Arrays.sort(b,(x,y)->f(x,y));
        for(int i=0;i<n;i++){
            ts.add(new int[]{b[i][0],b[i][1],i});
        }
        long[] pre=new long[n];pre[0]=b[0][0];
        for(int i=1;i<n;i++){
            pre[i]=b[i][0]+pre[i-1];
            //out.write(pre[i]+", ");
        }
        List<Integer> l=new ArrayList<>();
        int ok=-1;
        for(int i=0;i<n;i++){
            if(ok!=-1) break;
            int sum=b[i][0],idx=-1;
            while(true){
                int[] tmp=ts.lower(new int[]{sum+1,-1,-1});
                if(tmp==null) break;
                //out.write("loop "+tmp[0]+", "+tmp[1]+", "+tmp[2]+", "+sum+"\n");
                if(tmp[2]==n-1){ok=i;break;}
                if(tmp[2]<=idx) break;
                idx=tmp[2];
                sum=(int)Math.min(pre[tmp[2]],(int)2e9); 
            }
        }
        //out.write("ok- "+ok+", ");
        for(int i=ok;i<n;i++){
            l.add(b[i][1]);
        }
        Collections.sort(l);
        out.write(l.size()+"\n");
        for(int x:l)out.write((x+1)+" ");
        out.write("\n");
}
/*
 
*/
public static void main(String[] args) throws  IOException{
                assign();
                int t=int_v(read());
                while(t--!=0) solve();
                out.flush();
}

// taking inputs
static BufferedReader s1;
static BufferedWriter out;
static String read() throws IOException{String line="";while(line.length()==0){line=s1.readLine();continue;}return line;}
static int int_v (String s1){return Integer.parseInt(s1);}
static long long_v(String s1){return Long.parseLong(s1);}
static void sort(int[] a){List<Integer> l=new ArrayList<>();for(int x:a){l.add(x);}Collections.sort(l);for(int i=0;i<a.length;i++){a[i]=l.get(i);}}
static int[] int_arr() throws IOException{String[] a=read().split(" ");int[] b=new int[a.length];for(int i=0;i<a.length;i++){b[i]=int_v(a[i]);}return b;}
static long[] long_arr() throws IOException{String[] a=read().split(" ");long[] b=new long[a.length];for(int i=0;i<a.length;i++){b[i]=long_v(a[i]);}return b;}
static void assign(){s1=new BufferedReader(new InputStreamReader(System.in));out=new BufferedWriter(new OutputStreamWriter(System.out));}
//static String setpreciosion(double d,int k){BigDecimal d1 = new BigDecimal(Double.toString(d));return d1.setScale(k,RoundingMode.HALF_UP).toString();}//UP DOWN HALF_UP
static long gcd(long a,long b){if(b==0){return a;}return gcd(b,a%b);}
static long Modpow(long a,long p,long m){long res=1;while(p>0){if((p&1)!=0){res=(res*a)%m;}p >>=1;a=(a*a)%m;}return res%m;}
static long Modmul(long a,long b,long m){return ((a%m)*(b%m))%m;}
static long ModInv(long a,long m){return Modpow(a,m-2,m);}
//static long nck(int n,int r,long m){if(r>n){return 0l;}return Modmul(f[n],ModInv(Modmul(f[n-r],f[r],m),m),m);}
//static long[] f;
}