Given an array A of non-negative integers, return the maximum sum of elements in two non-overlapping (contiguous) subarrays, which have lengths L and M.  (For clarification, the L-length subarray could occur before or after the M-length subarray.)
Formally, return the largest V for which V = (A[i] + A[i+1] + ... + A[i+L-1]) + (A[j] + A[j+1] + ... + A[j+M-1]) and either:
0 <= i < i + L - 1 < j < j + M - 1 < A.length, or
0 <= j < j + M - 1 < i < i + L - 1 < A.length.
Example 1:
Input: A = [0,6,5,2,2,5,1,9,4], L = 1, M = 2
Output: 20
Explanation: One choice of subarrays is [9] with length 1, and [6,5] with length 2.
Example 2:
Input: A = [3,8,1,3,2,1,8,9,0], L = 3, M = 2
Output: 29
Explanation: One choice of subarrays is [3,8,1] with length 3, and [8,9] with length 2.
Example 3:
Input: A = [2,1,5,6,0,9,5,0,3,8], L = 4, M = 3
Output: 31
Explanation: One choice of subarrays is [5,6,0,9] with length 4, and [3,8] with length 3.
Note:
L >= 1
M >= 1
L + M <= A.length <= 1000
0 <= A[i] <= 1000
class Solution:
    def maxSumTwoNoOverlap(self, A: List[int], L: int, M: int) -> int:
        prefix_sum = [0] * (len(A) + 1)
        for i in range(len(A)): prefix_sum[i+1] = prefix_sum[i] + A[i]
        maxM = maxL = result = 0
        
        for i in range(M, len(prefix_sum) - L):
            # optimal for L-list start at i+1 and occur after M-list
            maxM = max(maxM, prefix_sum[i] - prefix_sum[i-M])
            result = max(result, maxM + prefix_sum[i+L] - prefix_sum[i])
            
        for i in range(L, len(prefix_sum) - M):
            # optimal for M-list start at i+1 and occur after L-list
            maxL = max(maxL, prefix_sum[i] - prefix_sum[i-L])
            result = max(result, maxL + prefix_sum[i+M] - prefix_sum[i])
            
        return result
class Solution:
    def maxSumTwoNoOverlap(self, A: List[int], L: int, M: int) -> int:
        prefix_sum = [0] * (len(A) + 1)
        for i in range(len(A)): prefix_sum[i+1] = prefix_sum[i] + A[i]
        maxM = maxL = result = 0
        
        for i in range(M, len(prefix_sum) - L):
            # optimal for L-list start at i+1 and occur after M-list
            maxM = max(maxM, prefix_sum[i] - prefix_sum[i-M])
            result = max(result, maxM + prefix_sum[i+L] - prefix_sum[i])
            
        for i in range(L, len(prefix_sum) - M):
            # optimal for M-list start at i+1 and occur after L-list
            maxL = max(maxL, prefix_sum[i] - prefix_sum[i-L])
            result = max(result, maxL + prefix_sum[i+M] - prefix_sum[i])
            
        return result