Buggy python submission (verdict: Time Limit Exceeded):
import sys

periphery, n = map(int, input().split())
xxx = list(map(int, sys.stdin.readlines()))
xxx.append(xxx[0] + periphery)
xxx.append(periphery - xxx[-2])
dp = [[0, 0] for _ in range(n + 1)]
for w in range(1, n):
    ndp = [[0, 0] for _ in range(n + 1)]
    for l in range(n - w):
        r = l + w
        pos_l, pos_l1, pos_r1, pos_r = xxx[l], xxx[l + 1], xxx[r - 1], xxx[r]
        pos_left_plant_left = dp[l + 1][0] + (pos_l1 - pos_l)
        pos_left_plant_right = dp[l][0] + (periphery - (pos_r - pos_l))
        pos_right_plant_left = dp[l + 1][1] + (periphery - (pos_r - pos_l))
        pos_right_plant_right = dp[l][1] + (pos_r - pos_r1)
        ndp[l][0] = max(pos_left_plant_left, pos_right_plant_left)
        ndp[l][1] = max(pos_left_plant_right, pos_right_plant_right)
    dp = ndp
print(max(dp[0][0] + xxx[0], dp[0][1] + xxx[-1]))


Fixed submission:
import sys
from itertools import accumulate

circumference, n = map(int, input().split())
lll = list(map(int, sys.stdin.readlines()))
rrr = [circumference - l for l in lll]
rrr.reverse()
lll = [0] + lll
rrr = [0] + rrr
acc_l = list(accumulate(lll))
acc_r = list(accumulate(rrr))

ans = max(lll[-1], rrr[-1])
for take_l in range(1, n):
    take_r = n - take_l

    # l last
    tmp_l = lll[take_l] + 2 * (acc_l[take_l - 1] + acc_r[take_r])
    # r last
    tmp_r = rrr[take_r] + 2 * (acc_r[take_r - 1] + acc_l[take_l])

    if take_l < take_r:
        tmp_l -= 2 * acc_r[take_r - take_l]
        tmp_r -= 2 * acc_r[take_r - 1 - take_l]
    elif take_l > take_r:
        tmp_l -= 2 * acc_l[take_l - 1 - take_r]
        tmp_r -= 2 * acc_l[take_l - take_r]

    ans = max(ans, tmp_l, tmp_r)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import sys

periphery, n = map(int, input().split())
xxx = list(map(int, sys.stdin.readlines()))
xxx.append(xxx[0] + periphery)
xxx.append(periphery - xxx[-2])
dp = [[0, 0] for _ in range(n + 1)]
for w in range(1, n):
    ndp = [[0, 0] for _ in range(n + 1)]
    for l in range(n - w):
        r = l + w
        pos_l, pos_l1, pos_r1, pos_r = xxx[l], xxx[l + 1], xxx[r - 1], xxx[r]
        pos_left_plant_left = dp[l + 1][0] + (pos_l1 - pos_l)
        pos_left_plant_right = dp[l][0] + (periphery - (pos_r - pos_l))
        pos_right_plant_left = dp[l + 1][1] + (periphery - (pos_r - pos_l))
        pos_right_plant_right = dp[l][1] + (pos_r - pos_r1)
        ndp[l][0] = max(pos_left_plant_left, pos_right_plant_left)
        ndp[l][1] = max(pos_left_plant_right, pos_right_plant_right)
    dp = ndp
print(max(dp[0][0] + xxx[0], dp[0][1] + xxx[-1]))


Fixed submission:
import sys
from itertools import accumulate

circumference, n = map(int, input().split())
lll = list(map(int, sys.stdin.readlines()))
rrr = [circumference - l for l in lll]
rrr.reverse()
lll = [0] + lll
rrr = [0] + rrr
acc_l = list(accumulate(lll))
acc_r = list(accumulate(rrr))

ans = max(lll[-1], rrr[-1])
for take_l in range(1, n):
    take_r = n - take_l

    # l last
    tmp_l = lll[take_l] + 2 * (acc_l[take_l - 1] + acc_r[take_r])
    # r last
    tmp_r = rrr[take_r] + 2 * (acc_r[take_r - 1] + acc_l[take_l])

    if take_l < take_r:
        tmp_l -= 2 * acc_r[take_r - take_l]
        tmp_r -= 2 * acc_r[take_r - 1 - take_l]
    elif take_l > take_r:
        tmp_l -= 2 * acc_l[take_l - 1 - take_r]
        tmp_r -= 2 * acc_l[take_l - take_r]

    ans = max(ans, tmp_l, tmp_r)
print(ans)