from sortedcontainers import SortedSet


class Solution:
    def minReverseOperations(
        self, n: int, p: int, banned: List[int], k: int
    ) -> List[int]:
        ans = [-1] * n
        ans[p] = 0
        ts = [SortedSet() for _ in range(2)]
        for i in range(n):
            ts[i % 2].add(i)
        ts[p % 2].remove(p)
        for i in banned:
            ts[i % 2].remove(i)
        ts[0].add(n)
        ts[1].add(n)
        q = deque([p])
        while q:
            i = q.popleft()
            mi = max(i - k + 1, k - i - 1)
            mx = min(i + k - 1, n * 2 - k - i - 1)
            s = ts[mi % 2]
            j = s.bisect_left(mi)
            while s[j] <= mx:
                q.append(s[j])
                ans[s[j]] = ans[i] + 1
                s.remove(s[j])
                j = s.bisect_left(mi)
        return ans
