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...
Using python3 can you solve the prior task?
assistant
#Here is Python code to find all such players.

class solution(): 
    def __init__(self, n, arr): 
        self.n = n 
        self.org = arr
        self.arr = sorted(arr)     

    def checker(self, l, r): 
        sum = 0 
        for i in range(0, l + 1): 
            sum += self.arr[i]      
            
        for i in range(l + 1, r + 1, 1): 
            if sum >= self.arr[i]: 
                sum += self.arr[i]
            else: 
                return False
        return True 

    def solve(self): 
        l = 0 
        r = self.n - 1 
        mid = (l + r) // 2

        result = -1

        while mid != l and mid != r: 
            if self.checker(mid, self.n - 1) == True: 
                r = mid 
            else:
                l = mid
            mid = (l + r) // 2

        if self.checker(r, self.n - 1) == True: 
            result = r

        if self.checker(l, self.n - 1) == True: 
            result = l
        
        for i in range(0, self.n): 
            if self.org[i] >= self.arr[result]: 
                yield (i + 1)
        
        print(self.n - 1 - result + 1)

for _ in range(0, int(input())): 
    print(*sorted(solution(int(input()), list(map(int, input().split()))).solve()), sep = ' ')