Given two integers total_elements and sequence_index, where total_elements represents the size of the set {1, 2, ..., total_elements}, and sequence_index represents the 1-based index, return the sequence_index-th permutation of the set in lexicographical order as a string.
Example 1
Input: total_elements=5, sequence_index=16
Output: 32541
Explanation: The 16th permutation of [1,2,3,4,5] in lexicographical order is 32541.
Example 2
Input: total_elements=2, sequence_index=2
Output: 21
Explanation: The 2nd permutation of [1,2] is 21.
Example 3
Input: total_elements=4, sequence_index=7
Output: 1432
Explanation: The 7th permutation of [1,2,3,4] is 1432.
Constraints
Case 1
Input: total_elements=3, sequence_index=5
Expected: 312
Case 2
Input: total_elements=4, sequence_index=12
Expected: 2431
Case 3
Input: total_elements=6, sequence_index=20
Expected: 146325