The triangle inequality fails when the sum of the two smallest sides is less than or equal to the largest side. Given a sorted array, the easiest bad triangle to find is `(i, i+1, n-1)` — take the two smallest elements and the largest element.

If `nums[0] + nums[1] > nums[n-1]`, then every triple satisfies the triangle inequality and no bad triangle exists (return -1). Otherwise, indices `(0, 1, n-1)` form a bad triangle.

The problem asks for any 1-based indices `(i, j, k)` with `i < j < k`. You do not need to find the longest or most degenerate bad triangle — the first one you find is sufficient.