Buggy python submission (verdict: Runtime Error):
from sys import stdin

n, k = [int(x) for x in stdin.readline().rstrip().split()]
v = list(map(int, input().split()))

l = [ [(0, [])]*(k+1) for _ in range(k+1)]

left=0
right=0
for i in range(k+1):
  left=0
  for j in range(k+1):
    if i==0 and j==0:
        continue
#    if k <= (left+right):
    if k < (i+j):
        break
    if j==0:
      item = v[(n-1)-right]
      right +=1
      l[i][j] = (l[i-1][j][0]+item,l[i-1][j][1]+[item])
      continue
    item = v[left]
    left +=1
    l[i][j] = (l[i][j-1][0]+item,l[i][j-1][1]+[item])

#for i in range(k+1):
#  print(l[i])

ans = 0
for i in range(k+1):
  for j in range(k+1):
    if k < (i+j):
      break
    value = l[i][j][0]
    if ( k != (i+j)):
        itemlist = l[i][j][1]
        itemlist.sort()
        #print(itemlist)
        for ii in range (k-(i+j)):
           if len(itemlist) <= ii:
               break
           if 0 < itemlist[ii]:
               break
           value -= itemlist[ii]
        #print(i,j,value)
    ans = max(ans, value)

print(ans)


Fixed submission:
from sys import stdin

n, k = [int(x) for x in stdin.readline().rstrip().split()]
v = list(map(int, input().split()))

l = [ [(0, [])]*(k+1) for _ in range(k+1)]

left=0
right=0
for i in range(k+1):
  left=0
  for j in range(k+1):
    if i==0 and j==0:
        continue
#    if k <= (left+right):
    if len(v) < (i+j):
        break
    if k < (i+j):
        break
    if j==0:
      item = v[(n-1)-right]
      right +=1
      l[i][j] = (l[i-1][j][0]+item,l[i-1][j][1]+[item])
      continue
    item = v[left]
    left +=1
    l[i][j] = (l[i][j-1][0]+item,l[i][j-1][1]+[item])

#for i in range(k+1):
#  print(l[i])

ans = 0
for i in range(k+1):
  for j in range(k+1):
    if k < (i+j):
      break
    value = l[i][j][0]
    if ( k != (i+j)):
        itemlist = l[i][j][1]
        itemlist.sort()
        #print(itemlist)
        for ii in range (k-(i+j)):
           if len(itemlist) <= ii:
               break
           if 0 < itemlist[ii]:
               break
           value -= itemlist[ii]
        #print(i,j,value)
    ans = max(ans, value)

print(ans)

Buggy python submission (verdict: Runtime Error):
from sys import stdin

n, k = [int(x) for x in stdin.readline().rstrip().split()]
v = list(map(int, input().split()))

l = [ [(0, [])]*(k+1) for _ in range(k+1)]

left=0
right=0
for i in range(k+1):
  left=0
  for j in range(k+1):
    if i==0 and j==0:
        continue
#    if k <= (left+right):
    if k < (i+j):
        break
    if j==0:
      item = v[(n-1)-right]
      right +=1
      l[i][j] = (l[i-1][j][0]+item,l[i-1][j][1]+[item])
      continue
    item = v[left]
    left +=1
    l[i][j] = (l[i][j-1][0]+item,l[i][j-1][1]+[item])

#for i in range(k+1):
#  print(l[i])

ans = 0
for i in range(k+1):
  for j in range(k+1):
    if k < (i+j):
      break
    value = l[i][j][0]
    if ( k != (i+j)):
        itemlist = l[i][j][1]
        itemlist.sort()
        #print(itemlist)
        for ii in range (k-(i+j)):
           if len(itemlist) <= ii:
               break
           if 0 < itemlist[ii]:
               break
           value -= itemlist[ii]
        #print(i,j,value)
    ans = max(ans, value)

print(ans)


Fixed submission:
from sys import stdin

n, k = [int(x) for x in stdin.readline().rstrip().split()]
v = list(map(int, input().split()))

l = [ [(0, [])]*(k+1) for _ in range(k+1)]

left=0
right=0
for i in range(k+1):
  left=0
  for j in range(k+1):
    if i==0 and j==0:
        continue
#    if k <= (left+right):
    if len(v) < (i+j):
        break
    if k < (i+j):
        break
    if j==0:
      item = v[(n-1)-right]
      right +=1
      l[i][j] = (l[i-1][j][0]+item,l[i-1][j][1]+[item])
      continue
    item = v[left]
    left +=1
    l[i][j] = (l[i][j-1][0]+item,l[i][j-1][1]+[item])

#for i in range(k+1):
#  print(l[i])

ans = 0
for i in range(k+1):
  for j in range(k+1):
    if k < (i+j):
      break
    value = l[i][j][0]
    if ( k != (i+j)):
        itemlist = l[i][j][1]
        itemlist.sort()
        #print(itemlist)
        for ii in range (k-(i+j)):
           if len(itemlist) <= ii:
               break
           if 0 < itemlist[ii]:
               break
           value -= itemlist[ii]
        #print(i,j,value)
    ans = max(ans, value)

print(ans)