Coinciding with the National Day of Rainbow Island, the king invited $n$ ministers to play a game with prizes. First, he made the $n$ ministers line up, with the king at the head of the line. The king had some gold coins, and he wanted to give them to his ministers. However, the king was worried about the unfair distribution, so there were $k$ extra opportunities after the distribution -- each extra opportunity could be exchanged for any of the two ministers' gold coins. The king thought it fair that the number of gold coins in the minister's hands increased from $1$ to $n$.
Can you help the king find the original gold coin sequence? To put it simply, construct a permutation of length $n$ such that the minimum number of swaps for the permutation to become ordered (from small to large) is $k$.
Note: A permutation is a sequence of numbers that contains consecutive numbers and is not repeated, e.g 4,3,2,1 or 4,5,3,1,2.