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
What is a Python code to find all such players?
assistant
#Here is Python code to find all such players.
t os
import sys
from io import BytesIO, IOBase

def main():
    for _ in range(int(input())):
        n=int(input())
        a=list(map(int,input().split()))
        l=list()
        for i,item in enumerate(a):
            l.append([item,i+1])
        # print(l)
        l.sort()
        ans=[0]*n
        ans[0]=l[0][0]
        for i in range(1,n):
            temp=l[i][0]
            if ans[i-1]<temp:
                ans[i]=temp+ans[i-1]
                ans[i-1]=0
            else:
                ans[i]=temp+ans[i-1]
        flag=1
        for i in range(n-1,-1,-1):
            if not flag:
                ans[i]=0
            elif ans[i]==0:
                flag=0
            else:
                pass
        # print(ans)
        
        final=[]
        temp=0
        flag=0
        for i in range(n):
            if flag:
                temp+=1
                final.append(l[i][1])
                continue
            if ans[i]!=0:
                flag=1
                temp+=1
                final.append(l[i][1])
        print(temp)
        final.sort()
        print(*final)

# region fastio

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b),...