A8344 | Lucky Permutation

A permutation is an ordered set of $n$ elements, where each integer from $1$ to $n$ occurs exactly once. The element of permutation in position with index $i$ is denoted as $a_{i}$ ( $1<=i<=n$ ). Permutation $a$ is lexicographically smaller that permutation $b$ if there is such a $i$ ( $1<=i<=n$ ), that $a_{i}<b_{i}$ , and for any $j$ ( $1<=j<i$ ) $a_{j}=b_{j}$ . Let's make a list of all possible permutations of $n$ elements and sort it in the order of lexicographical increasing. Then the lexicographically $k$ -th permutation is the $k$ -th element of this list of permutations.

In the first sample the permutation looks like that:

1 2 3 4 6 7 5

The only suitable position is 4.

In the second sample the permutation looks like that:

2 1 3 4

The only suitable position is 4.