Problem:
Score : 600 points

Problem Statement

There are N piles of stones. The i-th pile has A_i stones.

Aoki and Takahashi are about to use them to play the following game:

Starting with Aoki, the two players alternately do the following operation:

Operation: Choose one pile of stones, and remove one or more stones from it.

When a player is unable to do the operation, he loses, and the other player wins.

When the two players play optimally, there are two possibilities in this game: the player who moves first always wins, or the player who moves second always wins, only depending on the initial number of stones in each pile.

In such a situation, Takahashi, the second player to act, is trying to guarantee his win by moving at least zero and at most (A_1 - 1) stones from the 1-st pile to the 2-nd pile before the game begins.

If this is possible, print the minimum number of stones to move to guarantee his victory; otherwise, print -1 instead.

Constraints

2 \leq N \leq 300

1 \leq A_i \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

Print the minimum number of stones to move to guarantee Takahashi's win; otherwise, print -1 instead.

Sample Input 1

2
5 3

Sample Output 1

1

Without moving stones, if Aoki first removes 2 stones from the 1-st pile, Takahashi cannot win in any way.

If Takahashi moves 1 stone from the 1-st pile to the 2-nd before the game begins so that both piles have 4 stones, Takahashi can always win by properly choosing his actions.

Sample Input 2

2
3 5

Sample Output 2

-1

It is not allowed to move stones from the 2-nd pile to the 1-st.

Sample Input 3

3
1 1 2

Sample Output 3

-1

It is not allowed to move all stones from the 1-st pile.

Sample Input 4

8
10 9 8 7 6 5 4 3

Sample Output 4

3

Sample Input 5

3
4294967297 8589934593 12884901890

Sample Output 5

1

Watch out for overflows.

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

namespace ABC
{
    class ProgramF
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var aList = Console.ReadLine().Split(" ").Select(x => long.Parse(x)).ToList();

            var a0 = aList[0];
            var a1 = aList[1];
            var ans = 0L;

            var backXor = xor(n, aList);
            for (var i = 0L; i < a0; i++)
            {
                aList[0] = a0 - i;
                aList[1] = a1 + i;

                if (((a0 - i) ^ (a1 + i) ^ backXor) == 0)
                {
                    ans = i;
                    break;
                }
            }

            if (ans == 0)
            {
                ans = -1;
            }
            Console.WriteLine(ans);
        }

        // 最初の山と2つ目の山以外の排他的論理和
        static long xor(int n, List<long> list)
        {
            var result = 0L;
            for (var i = 2; i < n; i++)
            {
                result ^= list[i];
            }
            return result;
        }
    }
}