write a go solution for Description:
This is the hard version of the problem. The only difference between the versions is the constraints on a_i. You can make hacks only if both versions of the problem are solved.

Nene is fighting with n monsters, located in a circle. These monsters are numbered from 1 to n, and the i-th (1<=i<=n) monster's current energy level is a_i.

Since the monsters are too strong, Nene decided to fight with them using the Attack Your Neighbour spell. When Nene uses this spell, the following actions happen in the following order one by one:

- The 1-st monster attacks the 2-nd monster;
- The 2-nd monster attacks the 3-rd monster;
- ldots
- The (n-1)-th monster attacks the n-th monster;
- The n-th monster attacks the 1-st monster.

When the monster with energy level x attacks the monster with the energy level y, the energy level of the defending monster becomes max(0,y-x) (the energy level of the attacking monster remains equal to x).

Nene is going to use this spell 10^100 times and deal with the monsters that will still have a non-zero energy level herself. She wants you to determine which monsters will have a non-zero energy level once she will use the described spell 10^100 times.

Input Format:
Each test contains multiple test cases. The first line contains the number of test cases t (1<=t<=10^4). The description of test cases follows.

The first line contains a single integer n (2<=n<=2*10^5) — the number of monsters.

The second line contains n integers a_1,a_2,ldots,a_n (0<=a_i<=10^9) — the current energy levels of monsters.

It is guaranteed that the sum of n over all test cases does not exceed 2*10^5.

Output Format:
For each test case,

- in the first line output an integer m — the number of monsters with non-zero energy level after 10^100 uses of the spell;
- in the second line of output m integers i_1,i_2,ldots,i_m (1<=i_1<i_2<ldots<i_m<=n) — the indices of these monsters in the increasing order.

If m=0, you may either output an empty line or don't output it.

Note:
In the first test case, the following actions happen during the first 3 uses of the spell in this order:

- Nene uses the Attack Your Neighbour spell for the first time;
- the 1-st monster attacks the 2-nd monster, after the attack the energy level of the 2-nd monster becomes equal to max(0,5-2)=3;
- the 2-nd monster attacks the 3-rd monster, after the attack the energy level of the 3-rd monster becomes equal to max(0,3-3)=0;
- the 3-rd monster attacks the 1-st monster, after the attack the energy level of the 1-st monster becomes equal to max(0,2-0)=2;
- Nene uses the Attack Your Neighbour spell for the second time;
- the 1-st monster attacks the 2-nd monster, after the attack the energy level of the 2-nd monster becomes equal to max(0,3-2)=1;
- the 2-nd monster attacks the 3-rd monster, after the attack the energy level of the 3-rd monster becomes equal to max(0,0-1)=0;
- the 3-rd monster attacks the 1-st monster, after the attack the energy level of the 1-st monster becomes equal to max(0,2-0)=2;
- Nene uses the Attack Your Neighbour spell for the third time;
- the 1-st monster attacks the 2-nd monster, after the attack the energy level of the 2-nd monster becomes equal to max(0,1-2)=0;
- the 2-nd monster attacks the 3-rd monster, after the attack the energy level of the 3-rd monster becomes equal to max(0,0-0)=0;
- the 3-rd monster attacks the 1-st monster, after the attack the energy level of the 1-st monster becomes equal to max(0,2-0)=2.

After each of the next uses of the spell, energy levels of monsters do not change. Thus, only the 1-st monster has a non-zero energy level in the end.

In the second test case, both monsters initially have zero energy level.. Output only the code with no comments, explanation, or additional text.