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...
from  ... Give me a Python program to find all such players?
assistant
#Here is Python program to find all such players.
collections import Counter
import math
class Solution(object):
       
    def __init__(self):
        self.d={}
        
    def solve(self,vec):
        C= Counter(vec)
        keys= sorted(C.keys())
        max_key=keys[-1]
        composed_keys=[]
        loser_keys=-1 ##inclusion
        total=0
        for i in range(0,len(keys)-1):
            composed_keys.append(keys[i])
            total+=keys[i]*C[keys[i]]
            if(total<keys[i+1]):
                loser_keys=i
                
        if(loser_keys==-1):
            return set()
        
        return set(keys[:loser_keys+1])
            
        
                    
if __name__=="__main__":
    n_cases= int(raw_input().strip())
    for i in range(0,n_cases):
        T=Solution()
        n_num = int(raw_input().strip())
        vec=map(int,raw_input().split(" "))
        #print "vec=",vec
        #T=Solution()
        loser=T.solve(vec)
        
        ans=[]
        for i in range(0,len(vec)):
            if vec[i] in loser:
                continue
            ans.append(i+1)
        print len(ans)
        for item in ans:
            print item,
        print