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

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

in_n = lambda: int(readline())
in_nn = lambda: map(int, readline().split())
in_s = lambda: readline().rstrip().decode('utf-8')
in_nl = lambda: list(map(int, readline().split()))
in_nl2 = lambda H: [in_nl() for _ in range(H)]
in_map = lambda: [s == ord('.') for s in readline() if s != ord('\n')]
in_map2 = lambda H: [in_map() for _ in range(H)]
in_all = lambda: map(int, read().split())


def solve(N, W, ws, vs):
    # S[i] = (v, w): 価値v, 重さw
    *S, = zip(vs, ws)

    def make(S):
        T = {0: 0}
        for v, w in S:
            # 価値v, 重さw
            T0 = dict(T)
            for k, val in T.items():
                if k + w > W:
                    continue
                if k + w in T0:
                    T0[k + w] = max(T0[k + w], val + v)
                else:
                    T0[k + w] = val + v
            T = T0
        v = 0
        R = []
        for k in sorted(T):
            v = max(v, T[k])
            # (重さk, 重さk以下での価値の最大v)
            R.append((k, v))
        return R

    def solve(T0, T1):
        T0.sort()
        T1.sort(reverse=1)

        it = iter(T1)
        k1, v1 = next(it)
        yield 0
        for k0, v0 in T0:
            # 重さの和がW以下になるようにスライドする
            while k0 + k1 > W:
                k1, v1 = next(it)
            yield v0 + v1

    # ２つの集合に分けて、それぞれ全列挙
    T0 = make(S[:N // 2])
    T1 = make(S[N // 2:])

    # 2つの全列挙を元に解を求める
    return max(solve(T0, T1))


def main():

    N, K = in_nn()
    A = in_nl()

    max_num = max(K, max(A))
    bit_len = max_num.bit_length()

    ws = []
    vs = []

    sum_value = 0
    for i in range(bit_len):

        cnt = 0
        for j in range(N):
            cnt += (A[j] >> bit_len - i - 1) & 1

        n = 2 ** (bit_len - i - 1)
        if cnt < -(-N // 2):
            value = (N - 2 * cnt) * n
            weight = n
            vs.append(value)
            ws.append(weight)
        sum_value += cnt * n

    ret = solve(len(vs), K, ws, vs)
    print(sum_value + ret)


if __name__ == '__main__':
    main()


Fixed submission:
import sys

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

in_n = lambda: int(readline())
in_nn = lambda: map(int, readline().split())
in_s = lambda: readline().rstrip().decode('utf-8')
in_nl = lambda: list(map(int, readline().split()))
in_nl2 = lambda H: [in_nl() for _ in range(H)]
in_map = lambda: [s == ord('.') for s in readline() if s != ord('\n')]
in_map2 = lambda H: [in_map() for _ in range(H)]
in_all = lambda: map(int, read().split())


def solve(N, W, ws, vs):
    # S[i] = (v, w): 価値v, 重さw
    *S, = zip(vs, ws)

    def make(S):
        T = {0: 0}
        for v, w in S:
            # 価値v, 重さw
            T0 = dict(T)
            for k, val in T.items():
                if k + w > W:
                    continue
                if k + w in T0:
                    T0[k + w] = max(T0[k + w], val + v)
                else:
                    T0[k + w] = val + v
            T = T0
        v = 0
        R = []
        for k in sorted(T):
            v = max(v, T[k])
            # (重さk, 重さk以下での価値の最大v)
            R.append((k, v))
        return R

    def solve(T0, T1):
        T0.sort()
        T1.sort(reverse=1)

        it = iter(T1)
        k1, v1 = next(it)
        yield 0
        for k0, v0 in T0:
            # 重さの和がW以下になるようにスライドする
            while k0 + k1 > W:
                k1, v1 = next(it)
            yield v0 + v1

    # ２つの集合に分けて、それぞれ全列挙
    T0 = make(S[:N // 2])
    T1 = make(S[N // 2:])

    # 2つの全列挙を元に解を求める
    return max(solve(T0, T1))


def main():

    N, K = in_nn()
    A = in_nl()

    max_num = max(K, max(A))
    bit_len = max_num.bit_length()

    ws = []
    vs = []

    sum_value = 0
    for i in range(bit_len):

        cnt = 0
        for j in range(N):
            cnt += (A[j] >> bit_len - i - 1) & 1

        n = 2 ** (bit_len - i - 1)
        if cnt < -(-N // 2):
            value = (N - 2 * cnt) * n
            weight = n
            vs.append(value)
            ws.append(weight)
        sum_value += cnt * n

    ret = solve(len(vs), K, ws, vs)
    print(sum_value + ret)


if __name__ == '__main__':
    main()