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 CPP):

Solution:
#include<iostream>
#include<bits/stdc++.h>
#include<string.h>
#define MOD 998244353
#define INF 1000000000000000001
#define ll long long
#define vi vector<int>
#define vll vector<ll>
#define vpll vector<pair<ll,ll>>
#define vpi vector<pair<int,int>>
#define pb push_back
#define F first
#define S second
#define all(s) s.begin(),s.end()
#define ub upper_bound
#define lb lower_bound
#define bs binary_search
#define mkp make_pair
#define endl "\n"
#define cerr(x) cout <<#x <<" = "<< x << endl;
using namespace std;
ll gcd(ll a, ll b) {if (b == 0)return a; return gcd(b, a % b);}
ll lcm(ll a,ll b){return (a*b)/(gcd(a,b));}
void swap(int& a, int& b) { a=a^b; b=a^b; a=a^b; }
ll gcdVec(vll vec){
    ll res = vec[0];
    for(int i=1;i<vec.size();i++){
        res = gcd(res,vec[i]);
        if(res==1){
            return 1;
        }
    }
    return res;
} 
bool isPrime(ll n){
    if(n<=1) return 0;
    if(n<=3) return 1;
    if(n%2==0 || n%3 == 0) return 0;
    for(ll i=5; i*i<=n; i+=6) if(n%i==0 || n%(i+2)==0) return 0;
    return 1; 
} 
int mul(int x, int y)
{
    return (x * 1LL * y) % MOD;
}
int power(int x,int y)
{
    int res = 1;  
  
    while (y > 0)
    {
        if (y & 1)
            res = mul(res,x);
  
        y = y>>1; 
        x = mul(x,x);  
    }
    return res;
}

void solve(){
    ll n; cin>>n;
    vpll a(n+1);
    a[0]={0,0};
    for(int i=1;i<=n;i++){
        int x;
        cin>>x;
        a[i]={x,i};
    }
    vll sum(n+1);
    sort(all(a));
    
    vll ans; 
    sum[1]=a[1].F;
    for(int i=2;i<=n;i++){
        sum[i]=sum[i-1]+a[i].F;
    }
    ans.pb(a[n].S);
    for(ll i=n-1;i>=1;i--){
        if(sum[i] >= a[i+1].F){
            ans.pb(a[i].S);
        }
        else
            break;
    }
    
    sort(all(ans));
    cout<<ans.size()<<endl;
    for(int i=0;i<ans.size();i++){
        cout<<ans[i]<<" ";
    }
    cout<<endl;
}

int main(){
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
#ifndef LOCAL
    auto start_time = clock();
    cerr << setprecision(3) << fixed;
#endif
    ll ttt=1;
    cin>>ttt;
    while(ttt--){
        solve();
    }
#ifndef LOCAL
    auto end_time = clock();
    cerr << "Execution time: " << (end_time - start_time) * (int)1e3 / CLOCKS_PER_SEC << " ms\n";
#endif    
    return 0;
}