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

n, k = map(int, input().split())
lst = list(map(int, input().split()))

def heap_push(my_lst, a):
    heapq.heappush(my_lst, a)
    return my_lst


def dfs(k, lst, my_lst):
    if k == 0:
        return max(sum(my_lst), 0)
    
    if len(my_lst) == 0:
        a = dfs(k-1, lst[1:], heap_push(my_lst[:], lst[0]))
        b = dfs(k-1, lst[:-1], heap_push(my_lst[:], lst[-1]))
        return max(a, b)
                
    if len(lst) == 0:
        return dfs(k-1, lst + heapq.nsmallest(1,my_lst), my_lst[1:])
                
    else:
        a = dfs(k-1, lst[1:], heap_push(my_lst[:], lst[0]))
        b = dfs(k-1, lst[:-1], heap_push(my_lst[:], lst[-1]))
        
        c = dfs(k-1, lst + heapq.nsmallest(1,my_lst), my_lst[1:])
        d = dfs(k-1, heapq.nsmallest(1,my_lst) + lst, my_lst[1:])
        return max(a,b,c,d)
    
my_lst = []
heapq.heapify(my_lst)
print(dfs(k, lst, []))

Fixed submission:
n, k = map(int, input().split())
lst = list(map(int, input().split()))

res = 0
max_num = min(n, k)
for i in range(max_num+1):
    for j in range(max_num+1 - i):
        my_lst = []
        my_lst += lst[:i]
        if j != 0:
            my_lst += lst[-j:]
        
        s = sum(my_lst)
        sorted_my_lst = sorted(my_lst)
        #print('my_lst :', my_lst)
        for l in range(k- i - j):
            if len(my_lst) > l:
                if sorted_my_lst[l] < 0:
                    s -= sorted_my_lst[l]
        res = max(res, s)

print(res)

Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
lst = list(map(int, input().split()))

def heap_push(my_lst, a):
    heapq.heappush(my_lst, a)
    return my_lst


def dfs(k, lst, my_lst):
    if k == 0:
        return max(sum(my_lst), 0)
    
    if len(my_lst) == 0:
        a = dfs(k-1, lst[1:], heap_push(my_lst[:], lst[0]))
        b = dfs(k-1, lst[:-1], heap_push(my_lst[:], lst[-1]))
        return max(a, b)
                
    if len(lst) == 0:
        return dfs(k-1, lst + heapq.nsmallest(1,my_lst), my_lst[1:])
                
    else:
        a = dfs(k-1, lst[1:], heap_push(my_lst[:], lst[0]))
        b = dfs(k-1, lst[:-1], heap_push(my_lst[:], lst[-1]))
        
        c = dfs(k-1, lst + heapq.nsmallest(1,my_lst), my_lst[1:])
        d = dfs(k-1, heapq.nsmallest(1,my_lst) + lst, my_lst[1:])
        return max(a,b,c,d)
    
my_lst = []
heapq.heapify(my_lst)
print(dfs(k, lst, []))

Fixed submission:
n, k = map(int, input().split())
lst = list(map(int, input().split()))

res = 0
max_num = min(n, k)
for i in range(max_num+1):
    for j in range(max_num+1 - i):
        my_lst = []
        my_lst += lst[:i]
        if j != 0:
            my_lst += lst[-j:]
        
        s = sum(my_lst)
        sorted_my_lst = sorted(my_lst)
        #print('my_lst :', my_lst)
        for l in range(k- i - j):
            if len(my_lst) > l:
                if sorted_my_lst[l] < 0:
                    s -= sorted_my_lst[l]
        res = max(res, s)

print(res)

Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
lst = list(map(int, input().split()))

def dfs(k, lst, my_lst):
    if k == 0:
        return max(sum(my_lst), 0)
    if len(my_lst) == 0:
        a = dfs(k-1, lst[1:], my_lst + [lst[0]])
        b = dfs(k-1, lst[:-1], my_lst + [lst[-1]])
        return max(a, b)
    if len(lst) == 0:
        return dfs(k-1, lst + [min(my_lst)], sorted(my_lst)[1:])
    else:
        a = dfs(k-1, lst[1:], my_lst + [lst[0]])
        b = dfs(k-1, lst[:-1], my_lst + [lst[-1]])
        c = dfs(k-1, lst + [min(my_lst)], sorted(my_lst)[1:])
        d = dfs(k-1, [min(my_lst)] + lst, sorted(my_lst)[1:])
        return max(a,b,c,d)
    
print(dfs(k, lst, []))

Fixed submission:
n, k = map(int, input().split())
lst = list(map(int, input().split()))

res = 0
max_num = min(n, k)
for i in range(max_num+1):
    for j in range(max_num+1 - i):
        my_lst = []
        my_lst += lst[:i]
        if j != 0:
            my_lst += lst[-j:]
        
        s = sum(my_lst)
        sorted_my_lst = sorted(my_lst)
        #print('my_lst :', my_lst)
        for l in range(k- i - j):
            if len(my_lst) > l:
                if sorted_my_lst[l] < 0:
                    s -= sorted_my_lst[l]
        res = max(res, s)

print(res)

Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
lst = list(map(int, input().split()))

def dfs(k, lst, my_lst):
    if k == 0:
        return max(sum(my_lst), 0)
    if len(my_lst) == 0:
        a = dfs(k-1, lst[1:], my_lst + [lst[0]])
        b = dfs(k-1, lst[:-1], my_lst + [lst[-1]])
        return max(a, b)
    if len(lst) == 0:
        return dfs(k-1, lst + [min(my_lst)], sorted(my_lst)[1:])
    else:
        a = dfs(k-1, lst[1:], my_lst + [lst[0]])
        b = dfs(k-1, lst[:-1], my_lst + [lst[-1]])
        c = dfs(k-1, lst + [min(my_lst)], sorted(my_lst)[1:])
        d = dfs(k-1, [min(my_lst)] + lst, sorted(my_lst)[1:])
        return max(a,b,c,d)
    
print(dfs(k, lst, []))

Fixed submission:
n, k = map(int, input().split())
lst = list(map(int, input().split()))

res = 0
max_num = min(n, k)
for i in range(max_num+1):
    for j in range(max_num+1 - i):
        my_lst = []
        my_lst += lst[:i]
        if j != 0:
            my_lst += lst[-j:]
        
        s = sum(my_lst)
        sorted_my_lst = sorted(my_lst)
        #print('my_lst :', my_lst)
        for l in range(k- i - j):
            if len(my_lst) > l:
                if sorted_my_lst[l] < 0:
                    s -= sorted_my_lst[l]
        res = max(res, s)

print(res)