K-th Permutation Sequence of First N Natural Numbers

Determine the K-th permutation from a sequence of the first N natural numbers.

Input:

Integer T indicating the number of test cases followed by 'T' test cases. Each test case contains two space-separated integers: N and K.

Output:

An array representing the K-th permutation of the first N natural numbers for each test case.

Example:

Input:

2 3 3

Output:

[2, 1, 3]

Explanation:

The permutations for N = 3 are {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)}. The 3rd permutation is [2, 1, 3].

Constraints:

• 1 ≤ T ≤ 10
• 1 ≤ N ≤ 5 * 103
• 1 ≤ K ≤ min(N!, 5 * 103)

Time limit: 1 sec

Note:

No need for printing in solution; implement the function to return results.