human
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...
impor ... Write me a Python code to find all such players?
assistant
#Here is Python code to find all such players.
t math
from collections import defaultdict
 
DEBUG = True
 
def log(*args, **kwargs):
    if DEBUG:
        print(*args, **kwargs)
 
def rint():
    return int(input())
 
def rlist(f=int):
    return list(map(f, input().split()))
 
def rstr():
    return input()
 
class Solution:
 
    def __init__(self):
        self.result = []
        self.a = []
        
    def run(self):

        n = rint()
        a = rlist()
        tokens = defaultdict(list)
        for i in range(n):
            tokens[a[i]].append(i)

        possible = []
        current = 0

        s = sorted(tokens.keys())

        #log(tokens)
        #log(s)

        for i in range(len(s)):
            #log(i, s[i], tokens[s[i]], current, possible)
            if i == len(s) - 1:
                possible.extend(tokens[s[i]])
                continue
            if current + s[i]*(len(tokens[s[i]])) < s[i + 1]:
                possible = []
            else:
                possible.extend(tokens[s[i]])
            current += s[i]*(len(tokens[s[i]]))

        print(len(possible))
        return " ".join([str(x + 1) for x in sorted(possible)])
            

        
                
if __name__ == '__main__':
    
    t = int(input())
    s = Solution()
    #print(s.run())
    for i in range(t):
    #    s.run()
        print(s.run())