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:
//fold
#include <bits/stdc++.h>
using namespace std;
#define In_The_Name_Of_Allah_The_Merciful ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define Alhamdulillah return 0;
#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define F_OR(i, a, b, s) for (int i = (a) ; i < (b) ; i += (s))
#define F_OR1(e) F_OR(i, 0, e, 1)
#define F_OR2(i, e) F_OR(i, 0, e, 1)
#define F_OR3(i, b, e) F_OR(i, b, e, (b)<(e)?1:-1)
#define F_OR4(i, b, e, s) F_OR(i, b, e, s)
#define GET5(a, b, c, d, e, ...) e
#define F_ORC(...) GET5(__VA_ARGS__, F_OR4, F_OR3, F_OR2, F_OR1)
#define lp(...) F_ORC(__VA_ARGS__)(__VA_ARGS__)
#define each(a,x) for (auto& a: x)
#define pb push_back
#define ins insert
#define sz(v) (int) v.size()
typedef long long ll;
typedef long double ld;
const long double PI = acos(-1);
const int di[8] = {0 , 0 , 1 , -1 , 1 , 1 , -1 , -1};
const int dj[8] = {1 , -1 , 0 , 0 , 1 , -1 , 1 , -1};

ll FirstTrue (ll l,ll r,function<bool(ll)>f){
  while(l<r){
  ll mid=l+(r-l)/2;
  f(mid)?r=mid:l=mid+1;} 
  return l;
}
ll LastTrue(ll l,ll r,function<bool(ll)>f){
  while(l<r){
  ll mid=l+(r-l+1)/2;
  f(mid)?l=mid:r=mid-1;} 
  return l;
}
 
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}

template<class T> void re(complex<T>& x);
template<class T1, class T2> void re(pair<T1,T2>& p);
template<class T> void re(vector<T>& a);
template<class T, size_t SZ> void re(array<T,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(double& x) { string t; re(t); x = stod(t); }
void re(ld& x) { string t; re(t); x = stold(t); }
template<class Arg, class... Args> void re(Arg& first, Args&... rest) { 
  re(first); re(rest...); 
}

template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = complex<T>(a,b); }
template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.first,p.second); }
template<class T> void re(vector<T>& a) { lp(i,sz(a)) re(a[i]); }
template<class T, size_t SZ> void re(array<T,SZ>& a) { lp(i,SZ) re(a[i]); }

template<class T1, class T2> void pr(const pair<T1,T2>& x);
template<class T, size_t SZ> void pr(const array<T,SZ>& x);
template<class T> void pr(const vector<T>& x);
template<class T> void pr(const set<T>& x);
template<class T1, class T2> void pr(const map<T1,T2>& x);

template<class T> void pr(const T& x) { cout << x; }
template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) { 
  pr(first); pr(rest...); 
}

template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
  pr(x.first,' ',x.second); 
}
template<class T> void prContain(const T& x) {
  each(a,x) pr(a,' '); 
}
template<class T, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
template<class T> void pr(const vector<T>& x) { prContain(x); }
template<class T> void pr(const set<T>& x) { prContain(x); }
template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }

void ps() { cout << '\n'; } 
template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) { 
  pr(first," "); ps(rest...);
}    

string to_string(const string& s) {
  return '"' + s + '"';
}
 
string to_string(const char* s) {
  return to_string((string) s);
}
 
string to_string(const char& c) {
  char s[1] = {c};
  return to_string(s);
}
 
string to_string(bool b) {
  return (b ? "true" : "false");
}
 
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
 
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
 
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
 
void DBG() {
    cerr << "]" << endl;
}
template<class H, class... T> void DBG(H h, T... t) {
  cerr << to_string(h);
  if(sizeof...(t))
      cerr << ", ";
  DBG(t...);
}

#ifndef ONLINE_JUDGE
#define debug(...) cerr << "[" << #__VA_ARGS__ << "] : [", DBG(__VA_ARGS__)
#else
#define debug(...) 0
#endif
//endfold



void Suhaib_Sawalha (){

	// late 10 min
	int n;
	re(n);
	map<ll, ll> mp, win;
	vector<ll> a(n);
	re(a);
	lp(n) ++mp[a[i]];
	vector<array<ll, 2>> k;
	ll s = 0;
	each(e,mp) {
		s += e.first * e.second;
		k.pb({e.first, e.first * e.second});
	}
	reverse(all(k));
	int last_win = 0;
	lp(sz(k)) {
		// ps(s);
		if (s >= last_win) {
			last_win = k[i][0];
			win[k[i][0]] = 1;
		}
		s -= k[i][1];
	}
	vector<int> w;
	lp(n) {
		if (win[a[i]]) {
			w.pb(i+1);
		}
	}
	ps(sz(w));
	pr(w);

}

int main(){
                                In_The_Name_Of_Allah_The_Merciful   /* بسم الله الرحمن الرحيم  */
#ifndef ONLINE_JUDGE
    freopen("SuhaibSawalha1","r",stdin);
#endif
int _;cin>>_;for(int i=1;i<=_;++i,cout<<'\n')
        // cout<<"Case #"<<i<<":\n", 
        Suhaib_Sawalha();
                                         Alhamdulillah                    /* الحمد لله */
}