Hello! We are given an integer N, The set [1,2,3,…,N] contains a total of N! unique permutations.

By listing and labeling all of the permutations in order, We get the following sequence (ie, for n = 3 ) :

1. "123"
2. "132"
3. "213"
4. "231"
5. "312"
6. "321"

Given n and k, return the kth permutation sequence.

For example, given n = 3, k = 4, ans = "231"

if n = 11, k = 1, ans = "1234567891011"

In this case, k will be a positive integer that is less than INT_MAX. n is reasonable enough to make sure the answer does not bloat up a lot.

N can be upto 1000 , k can be upto 1000.

How to solve it, simple backtracking will time out after N>10.