permutation sequence

def fact(n)
  return n if (n < 3)
  ans = 1
  n.downto(2) { |x|
    ans *= x
  }
  return ans
end


def get_permutation(n, k, nums = (1..n).to_a)
  answer = []
  remaining = k-1
  (n-1).downto(0) { |x|
    perms = fact(x)
    index = perms == 0 ? remaining : (remaining / perms).ceil
    answer.push(nums.slice!(index))
    remaining -= perms * index
  }
  return answer.join("")
end