Buggy python submission (verdict: Time Limit Exceeded):
N,K = map(int, input().split())
V = [int(v) for v in input().split()]


def f(L, i, n):
    if i == 0 or len(L) == 0:
        return 0
    if L[n] >= 0:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        return t+f(L,i-1,n)
    else:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        if i >= 2:
            return max(f(L, i-2, n), t+f(L, i-1, n))
        else:
            return t+f(L, i-1, n)
    

t = min(K+1, N)
L1 = [0]*(t)
L2 = [0]*(t)
cnt1 = 0
cnt2 = 0
for j in range(t):
    if V[j] <= 0:
        cnt1 += 1
    if cnt1 <= j:
        L1[j] = f(V, j, 0)
    if V[t-j-1] <= 0:
        cnt2 += 1
    if cnt2 <= j:
        L2[t-j-1] = f(V, t-j-1, -1)
    
V_sort = sorted(V)
s = sum(V)
ans = 0
for i in range(1, K+1):
    if i >= N:
        c = s
        j = 0
        while j < N:
            if V_sort[j] < 0:
                c -= V_sort[j]
            else:
                j = N
            j += 1
        ans = max(ans, c)
    else:
        c = 0
        for j in range(i+1):
            c = max(c, L1[j]+L2[i-j])
        ans = max(ans, c)
        
print(ans)

Fixed submission:
N,K = map(int, input().split())
V = [int(v) for v in input().split()]

ans = 0
for i in range(K+1):
    if i < N:
        for j in range(i+1):
            temp1 = V[:j]
            temp2 = V[N-(i-j):]
            temp = temp1 + temp2
            temp.sort()
            s = sum(temp)
            k = 0
            while k < len(temp) and k < K-i:
                if temp[k] < 0:
                    s -= temp[k]
                k += 1
            ans = max(ans, s)
    else:
        temp = sorted(V)
        s = sum(temp)
        j = 0
        while j < min(N, i-N):
            if temp[j] < 0:
                s -= temp[j]
            j += 1
        ans = max(ans, s)
        
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N,K = map(int, input().split())
V = [int(v) for v in input().split()]


def f(L, i, n):
    if i == 0 or len(L) == 0:
        return 0
    if L[n] >= 0:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        return t+f(L,i-1,n)
    else:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        if i >= 2:
            return max(f(L, i-2, n), t+f(L, i-1, n))
        else:
            return t+f(L, i-1, n)
    

t = min(K+1, N)
L1 = [0]*(t)
L2 = [0]*(t)
for j in range(t):
    L1[j] = f(V, j, 0)
    L2[t-j-1] = f(V, t-j-1, -1)
    
V_sort = sorted(V)
s = sum(V)
ans = 0
for i in range(1, K+1):
    if i >= N:
        c = s
        j = 0
        while j < N:
            if V_sort[j] < 0:
                c -= V_sort[j]
            else:
                j = N
            j += 1
        ans = max(ans, c)
    else:
        c = 0
        for j in range(i+1):
            c = max(c, L1[j]+L2[i-j])
        ans = max(ans, c)
        
print(ans)

Fixed submission:
N,K = map(int, input().split())
V = [int(v) for v in input().split()]

ans = 0
for i in range(K+1):
    if i < N:
        for j in range(i+1):
            temp1 = V[:j]
            temp2 = V[N-(i-j):]
            temp = temp1 + temp2
            temp.sort()
            s = sum(temp)
            k = 0
            while k < len(temp) and k < K-i:
                if temp[k] < 0:
                    s -= temp[k]
                k += 1
            ans = max(ans, s)
    else:
        temp = sorted(V)
        s = sum(temp)
        j = 0
        while j < min(N, i-N):
            if temp[j] < 0:
                s -= temp[j]
            j += 1
        ans = max(ans, s)
        
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N,K = map(int, input().split())
V = [int(v) for v in input().split()]


def f(L, i, n):
    if i == 0 or len(L) == 0:
        return 0
    if L[n] >= 0:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        return t+f(L,i-1,n)
    else:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        if i >= 2:
            return max(f(L, i-2, n), t+f(L, i-1, n))
        else:
            return t+f(L, i-1, n)
    

V_sort = sorted(V)
s = sum(V)
ans = 0
for i in range(1, K+1):
    if i >= N:
        c = s
        j = 0
        while j < N:
            if V_sort[j] < 0:
                c -= V_sort[j]
            else:
                j = N
            j += 1
        ans = max(ans, c)
    else:
        c = 0
        for j in range(i+1):
            c = max(c, f(V, j, 0)+f(V, i-j, -1))
        ans = max(ans, c)
        
print(ans)

Fixed submission:
N,K = map(int, input().split())
V = [int(v) for v in input().split()]

ans = 0
for i in range(K+1):
    if i < N:
        for j in range(i+1):
            temp1 = V[:j]
            temp2 = V[N-(i-j):]
            temp = temp1 + temp2
            temp.sort()
            s = sum(temp)
            k = 0
            while k < len(temp) and k < K-i:
                if temp[k] < 0:
                    s -= temp[k]
                k += 1
            ans = max(ans, s)
    else:
        temp = sorted(V)
        s = sum(temp)
        j = 0
        while j < min(N, i-N):
            if temp[j] < 0:
                s -= temp[j]
            j += 1
        ans = max(ans, s)
        
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N,K = map(int, input().split())
V = [int(v) for v in input().split()]


def f(L, i, n):
    if i == 0 or len(L) == 0:
        return 0
    if L[n] >= 0:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        return t+f(L,i-1,n)
    else:
        t = L[n]
        if n >= 0:
            n += 1
        else:
            n -= 1
        if i >= 2:
            return max(f(L, i-2, n), t+f(L, i-1, n))
        else:
            return t+f(L, i-1, n)
    
V_sort = sorted(V)
s = sum(V)
ans = 0
for i in range(1, K+1):
    if i >= N:
        c = s
        j = 0
        while j < N:
            if V_sort[j] < 0:
                c -= V_sort[j]
            else:
                j = N
            j += 1
        ans = max(ans, c)
    else:
        c = 0
        for j in range(i+1):
            c = max(c, f(V, j, 0)+f(V, i-j, -1))
        ans = max(ans, c)
        
print(ans)

Fixed submission:
N,K = map(int, input().split())
V = [int(v) for v in input().split()]

ans = 0
for i in range(K+1):
    if i < N:
        for j in range(i+1):
            temp1 = V[:j]
            temp2 = V[N-(i-j):]
            temp = temp1 + temp2
            temp.sort()
            s = sum(temp)
            k = 0
            while k < len(temp) and k < K-i:
                if temp[k] < 0:
                    s -= temp[k]
                k += 1
            ans = max(ans, s)
    else:
        temp = sorted(V)
        s = sum(temp)
        j = 0
        while j < min(N, i-N):
            if temp[j] < 0:
                s -= temp[j]
            j += 1
        ans = max(ans, s)
        
print(ans)