Please solve the programming task below using a self-contained code snippet in a markdown code block.

You are given two 0-indexed integer arrays nums1 and nums2 of the same length. A pair of indices (i,j) is called beautiful if|nums1[i] - nums1[j]| + |nums2[i] - nums2[j]| is the smallest amongst all possible indices pairs where i < j.
Return the beautiful pair. In the case that there are multiple beautiful pairs, return the lexicographically smallest pair.
Note that

|x| denotes the absolute value of x.
A pair of indices (i1, j1) is lexicographically smaller than (i2, j2) if i1 < i2 or i1 == i2 and j1 < j2.

 
Please complete the following python code precisely:
```python
class Solution:
    def beautifulPair(self, nums1: List[int], nums2: List[int]) -> List[int]:
```