# 1533. Find the Index of the Large Integer

<https://leetcode.com/problems/find-the-index-of-the-large-integer>

## Description

We have an integer array `arr`, where all the integers in `arr` are equal except for one integer which is **larger** than the rest of the integers. You will not be given direct access to the array, instead, you will have an **API** `ArrayReader` which have the following functions:

* `int compareSub(int l, int r, int x, int y)`: where `0 <= l, r, x, y < ArrayReader.length()`, `l <= r and` `x <= y`. The function compares the sum of sub-array `arr[l..r]` with the sum of the sub-array `arr[x..y]` and returns:
  * **1** if `arr[l]+arr[l+1]+...+arr[r] > arr[x]+arr[x+1]+...+arr[y]`.
  * **0** if `arr[l]+arr[l+1]+...+arr[r] == arr[x]+arr[x+1]+...+arr[y]`.
  * **-1** if `arr[l]+arr[l+1]+...+arr[r] < arr[x]+arr[x+1]+...+arr[y]`.
* `int length()`: Returns the size of the array.

You are allowed to call `compareSub()` **20 times** at most. You can assume both functions work in `O(1)` time.

Return *the index of the array `arr` which has the largest integer*.

**Follow-up:**

* What if there are two numbers in `arr` that are bigger than all other numbers?
* What if there is one number that is bigger than other numbers and one number that is smaller than other numbers?

**Example 1:**

```
**Input:** arr = [7,7,7,7,10,7,7,7]
**Output:** 4
**Explanation:** The following calls to the API
reader.compareSub(0, 0, 1, 1) // returns 0 this is a query comparing the sub-array (0, 0) with the sub array (1, 1), (i.e. compares arr[0] with arr[1]).
Thus we know that arr[0] and arr[1] doesn't contain the largest element.
reader.compareSub(2, 2, 3, 3) // returns 0, we can exclude arr[2] and arr[3].
reader.compareSub(4, 4, 5, 5) // returns 1, thus for sure arr[4] is the largest element in the array.
Notice that we made only 3 calls, so the answer is valid.
```

**Example 2:**

```
**Input:** nums = [6,6,12]
**Output:** 2
```

**Constraints:**

* `2 <= arr.length <= 5 * 10^5`
* `1 <= arr[i] <= 100`
* All elements of `arr` are equal except for one element which is larger than all other elements.

## ac

```java
```