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


def solve(n, aaa):
    if n == 2:
        h, m = divmod(sum(aaa), 2)
        if m == 1 or h > aaa[0]:
            return -1
        return aaa[0] - h

    x = 0
    for a in aaa[2:]:
        x ^= a
    a0, a1 = aaa[:2]
    s = a0 + a1

    if s & 1 != x & 1:
        return -1

    p, q = 0, 0

    b = 1 << 40
    while b:
        bx = x & b
        if bx == 0:
            # print('bx', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()
            if s >= 2 * b:
                if p + b <= a0:
                    p |= b
                    q |= b
                    s -= 2 * b
                # else:
                #     return -1
        else:
            if s < b:
                return -1
            if p + b <= a0 and q + b > a1:
                p |= b
            else:
                q |= b
            s -= b

        # print(f'{b:040b}')
        # print(f'{p:040b}')
        # print(f'{q:040b}')
        # print(f'{a0:040b}')
        # print(f'{a1:040b}')
        # print()

        b >>= 1

    if p == 0:
        return -1
    assert s == 0
    assert p ^ q == x
    assert a0 - p == q - a1
    return a0 - p


n, *aaa = map(int, sys.stdin.buffer.read().split())
print(solve(n, aaa))


Fixed submission:
import sys


def solve(n, aaa):
    if n == 2:
        h, m = divmod(sum(aaa), 2)
        if m == 1 or h > aaa[0]:
            return -1
        return aaa[0] - h

    x = 0
    for a in aaa[2:]:
        x ^= a
    a0, a1 = aaa[:2]
    s = a0 + a1

    if s & 1 != x & 1:
        return -1

    p, q = 0, 0

    b = 1 << 40
    swappable = []
    while b:
        bx = x & b
        if bx == 0:
            # print('bx=0', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()
            if s >= 2 * b:
                if p | b <= a0:
                    p |= b
                    q |= b
                    s -= 2 * b
                elif swappable:
                    bs = swappable.pop()
                    p ^= bs
                    q ^= bs
                    p |= b
                    q |= b
                    s -= 2 * b
                else:
                    return -1
        else:
            if s < b:
                return -1
            if p | b <= a0 and q | b > a1:
                p |= b
                swappable.append(b)
            else:
                q |= b
            s -= b

            # print('bx=1', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()

        b >>= 1

    if p == 0:
        return -1
    assert s == 0
    assert p ^ q == x
    assert a0 - p == q - a1
    return a0 - p


n, *aaa = map(int, sys.stdin.buffer.read().split())
print(solve(n, aaa))

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


def solve(n, aaa):
    if n == 2:
        h, m = divmod(sum(aaa), 2)
        if m == 1 or h > aaa[0]:
            return -1
        return aaa[0] - h

    x = 0
    for a in aaa[2:]:
        x ^= a
    a0, a1 = aaa[:2]
    s = a0 + a1

    if s & 1 != x & 1:
        return -1

    p, q = 0, 0

    b = 1 << 40
    while b:
        bx = x & b
        if bx == 0:
            # print('bx', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()
            if s >= 2 * b:
                if p + b <= a0:
                    p |= b
                    q |= b
                    s -= 2 * b
                else:
                    raise RuntimeError
                    # return -1
        else:
            if s < b:
                return -1
            if p + b <= a0 and q + b > a1:
                p |= b
            else:
                q |= b
            s -= b

        # print(f'{b:040b}')
        # print(f'{p:040b}')
        # print(f'{q:040b}')
        # print(f'{a0:040b}')
        # print(f'{a1:040b}')
        # print()

        b >>= 1

    if p == 0:
        return -1
    assert s == 0
    assert p ^ q == x
    assert a0 - p == q - a1
    return a0 - p


n, *aaa = map(int, sys.stdin.buffer.read().split())
print(solve(n, aaa))


Fixed submission:
import sys


def solve(n, aaa):
    if n == 2:
        h, m = divmod(sum(aaa), 2)
        if m == 1 or h > aaa[0]:
            return -1
        return aaa[0] - h

    x = 0
    for a in aaa[2:]:
        x ^= a
    a0, a1 = aaa[:2]
    s = a0 + a1

    if s & 1 != x & 1:
        return -1

    p, q = 0, 0

    b = 1 << 40
    swappable = []
    while b:
        bx = x & b
        if bx == 0:
            # print('bx=0', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()
            if s >= 2 * b:
                if p | b <= a0:
                    p |= b
                    q |= b
                    s -= 2 * b
                elif swappable:
                    bs = swappable.pop()
                    p ^= bs
                    q ^= bs
                    p |= b
                    q |= b
                    s -= 2 * b
                else:
                    return -1
        else:
            if s < b:
                return -1
            if p | b <= a0 and q | b > a1:
                p |= b
                swappable.append(b)
            else:
                q |= b
            s -= b

            # print('bx=1', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()

        b >>= 1

    if p == 0:
        return -1
    assert s == 0
    assert p ^ q == x
    assert a0 - p == q - a1
    return a0 - p


n, *aaa = map(int, sys.stdin.buffer.read().split())
print(solve(n, aaa))

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


def solve(n, aaa):
    if n == 2:
        h, m = divmod(sum(aaa), 2)
        if m == 1 or h > aaa[0]:
            return -1
        return aaa[0] - h

    x = 0
    for a in aaa[2:]:
        x ^= a
    a0, a1 = aaa[:2]
    s = a0 + a1

    if s & 1 != x & 1:
        return -1

    p, q = 0, 0

    b = 1 << 40
    while b:
        bx = x & b
        if bx == 0:
            # print('bx', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()
            if s >= 2 * b:
                if p + b <= a0:
                    p |= b
                    q |= b
                    s -= 2 * b
                else:
                    return -1
        else:
            if s < b:
                return -1
            if p + b <= a0 and q + b > a1:
                p |= b
            else:
                q |= b
            s -= b

        # print(f'{b:040b}')
        # print(f'{p:040b}')
        # print(f'{q:040b}')
        # print(f'{a0:040b}')
        # print(f'{a1:040b}')
        # print()

        b >>= 1

    if p == 0:
        return -1
    assert s == 0
    assert p ^ q == x
    assert a0 - p == q - a1
    return a0 - p


n, *aaa = map(int, sys.stdin.buffer.read().split())
ans = solve(n, aaa)
if ans == -1:
    raise RuntimeError
print(solve(n, aaa))


Fixed submission:
import sys


def solve(n, aaa):
    if n == 2:
        h, m = divmod(sum(aaa), 2)
        if m == 1 or h > aaa[0]:
            return -1
        return aaa[0] - h

    x = 0
    for a in aaa[2:]:
        x ^= a
    a0, a1 = aaa[:2]
    s = a0 + a1

    if s & 1 != x & 1:
        return -1

    p, q = 0, 0

    b = 1 << 40
    swappable = []
    while b:
        bx = x & b
        if bx == 0:
            # print('bx=0', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()
            if s >= 2 * b:
                if p | b <= a0:
                    p |= b
                    q |= b
                    s -= 2 * b
                elif swappable:
                    bs = swappable.pop()
                    p ^= bs
                    q ^= bs
                    p |= b
                    q |= b
                    s -= 2 * b
                else:
                    return -1
        else:
            if s < b:
                return -1
            if p | b <= a0 and q | b > a1:
                p |= b
                swappable.append(b)
            else:
                q |= b
            s -= b

            # print('bx=1', s)
            # print(f'{b:040b}')
            # print(f'{p:040b}')
            # print(f'{q:040b}')
            # print(f'{a0:040b}')
            # print(f'{a1:040b}')
            # print()

        b >>= 1

    if p == 0:
        return -1
    assert s == 0
    assert p ^ q == x
    assert a0 - p == q - a1
    return a0 - p


n, *aaa = map(int, sys.stdin.buffer.read().split())
print(solve(n, aaa))