Buggy python submission (verdict: Runtime Error):
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Fixed submission:
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L and m >=0:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Buggy python submission (verdict: Runtime Error):
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = 0
        m = M
        while 2**m > K-L:
            R += (N-r_list[m])*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    L, M = hard_log2(K)
    R = 0
    for i in range(M+1, 41):
        R += r_list[i]*(2**i)
    return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)

    
    print(res)

Fixed submission:
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L and m >=0:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Buggy python submission (verdict: Runtime Error):
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = 0
        m = M
        while 2**m > K-L:
            R += (N-r_list[m])*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*40
    for i in range(40):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(40):
            R += r_list[i]*(2**i)
        return R
    L, M = hard_log2(K)
    R = 0
    for i in range(M+1, 40):
        R += r_list[i]*(2**i)
    return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)

    
    print(res)

Fixed submission:
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L and m >=0:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Buggy python submission (verdict: Runtime Error):
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[M], N - r_list[M])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = 0
        m = M
        while 2**m > K-L:
            R += (N-r_list[m])*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*40
    for i in range(40):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(40):
            R += r_list[i]*(2**i)
        return R
    L, M = hard_log2(K)
    R = 0
    for i in range(M+1, 40):
        R += r_list[i]*(2**i)
    return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Fixed submission:
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L and m >=0:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Buggy python submission (verdict: Runtime Error):
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[M], N - r_list[M])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = 0
        while 2**M > K-L:
            R += (N-r_list[M])*(2**M)
            M -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*40
    for i in range(40):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(40):
            R += r_list[i]*(2**i)
        return R
    L, M = hard_log2(K)
    R = 0
    for i in range(M+1, 40):
        R += r_list[i]*(2**i)
    return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Fixed submission:
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L and m >=0:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Buggy python submission (verdict: Runtime Error):
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[M], N - r_list[M])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = 0
        while 2**M > K-L:
            R += (N-r_list[M])*(2**M)
            M -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*40
    for i in range(40):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(40):
            R += r_list[i]*(2**i)
        return R
    L, M = hard_log2(K)
    R = 0
    for i in range(M+1, 40):
        R += r_list[i]*(2**i)
    return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Fixed submission:
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L and m >=0:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Buggy python submission (verdict: Runtime Error):
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = 0
        while 2**M > K-L:
            R += (N-r_list[M])*(2**M)
            M -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize(r_list, L-1, N))

def main_d(A_list, N, K):
    r_list = [0]*40
    for i in range(40):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    L, M = hard_log2(K)
    R = 0
    for i in range(M+1, 40):
        R += r_list[i]*(2**i)
    return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Fixed submission:
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L and m >=0:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Buggy python submission (verdict: Runtime Error):
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = 0
        while 2**M > K-L:
            R += (N-r_list[M])*(2**M)
            M -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize(r_list, L-1, N))

def main_d(A_list, N, K):
    r_list = [0]*40
    for i in range(40):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    L, M = hard_log2(K)
    R = 0
    for i in range(N+1, 40):
        R += r_list[i]*(2**i)
    return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)

Fixed submission:
# D

# 10^12 < 2^40

def hard_log2(N):
    
    r = 1
    l = 0
    while N >= 2*r:
        r *= 2
        l += 1
    return r, l

def maximize_simple(r_list, K, N):
    if K == 0:
        return 0
    R = 0
    L, M = hard_log2(K)
    for i in range(M+1):
        R += max(r_list[i], N - r_list[i])*(2**i)
        
    return R

def maximize(r_list, K, N):
    
    if K == 0:
        return 0
    
    L, M = hard_log2(K)
    
    if r_list[M] >= N - r_list[M]:
        return maximize_simple(r_list, L-1, N)+r_list[M]*(2**M)
    else:
        R = (N-r_list[M])*(2**M)
        m = M - 1
        while 2**m > K-L and m >=0:
            R += r_list[m]*(2**m)
            m -= 1
        
        return max(maximize(r_list, K-L, N)+R, maximize_simple(r_list, L-1, N)+r_list[M]*(2**M))

def main_d(A_list, N, K):
    r_list = [0]*41
    for i in range(41):
        for A in A_list:
            if (A % 2**(i+1)) >= 2**i:
                r_list[i] += 1
    if K == 0:
        R = 0
        for i in range(41):
            R += r_list[i]*(2**i)
        return R
    else:
        L, M = hard_log2(K)
        R = 0
        for i in range(M+1, 41):
            R += r_list[i]*(2**i)
        return R + maximize(r_list, K, N)
    

if __name__ == "__main__":
    N, K = map(int, input().split())
    A_list = list(map(int, input().split()))
    res = main_d(A_list, N, K)
    print(res)