56. Permutation Sequence

HardMath

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 for n = 3: "123", "132", "213", "231", "312", "321". Given n and k, return the k-th permutation sequence.

Examples

Input: 4 9

Output: 2314

Explanation: The 9th permutation of [1,2,3,4] in lexicographic order.

Constraints

  • 1 <= n <= 9
  • 1 <= k <= n!
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