from typing import List


class Solution:
    def maxNumber(self, nums1: List[int], nums2: List[int], k: int) -> List[int]:
        def pick(arr: List[int], t: int) -> List[int]:
            drop = len(arr) - t
            st = []
            for x in arr:
                while drop and st and st[-1] < x:
                    st.pop()
                    drop -= 1
                st.append(x)
            return st[:t]

        def greater(a: List[int], i: int, b: List[int], j: int) -> bool:
            while i < len(a) and j < len(b) and a[i] == b[j]:
                i += 1
                j += 1
            if j == len(b):
                return True
            if i < len(a) and a[i] > b[j]:
                return True
            return False

        def merge(a: List[int], b: List[int]) -> List[int]:
            i = j = 0
            res = []
            while i < len(a) or j < len(b):
                if greater(a, i, b, j):
                    res.append(a[i])
                    i += 1
                else:
                    res.append(b[j])
                    j += 1
            return res

        m, n = len(nums1), len(nums2)
        ans = []
        for i in range(max(0, k - n), min(k, m) + 1):
            a = pick(nums1, i)
            b = pick(nums2, k - i)
            cand = merge(a, b)
            if not ans or cand > ans:
                ans = cand
        return ans