You are given two coding problems from the same interview round. **Problem 1: Split a gold chain fairly** An array `weights` represents the weights of consecutive links in a gold chain. You must perform the following steps: 1. Remove exactly one link. 2. Reconnect the remaining links, preserving their relative order. 3. Cut the reconnected chain once so that it becomes two non-empty contiguous parts. Return `true` if there exists a choice of removed index `r` and cut position `k` in the new array such that the two resulting parts have the same total weight. Otherwise, return `false`. Formally, after removing `weights[r]`, the new array is: - `weights[0], weights[1], ..., weights[r-1], weights[r+1], ..., weights[n-1]` You need to determine whether there exists a cut position `k` in this new array such that: - sum of elements from index `0` to `k` equals the sum of elements from `k+1` to the end. **Follow-up:** Return all valid `(r, k)` pairs, where `r` is the removed index in the original array and `k` is the cut index in the array after removal. --- **Problem 2: Maximize a subarray whose endpoints are equal** Given an integer array `a`, find indices `i` and `j` such that: - `0 <= i <= j < n` - `a[i] == a[j]` - the value of `a[i] + a[i+1] + ... + a[j]` is maximized Return one pair `(i, j)` that achieves the maximum sum. **Follow-up:** Solve the problem using strictly `O(1)` extra space, even if a higher time complexity is allowed.