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++ (GCC 9.2.1) (judge verdict: Accepted)

#define _CRT_SECURE_NO_WARNINGS 1

#include <set>
#include <map>
#include <stack>
#include <queue>
#include <cmath>
#include <ctime>
#include <vector>
#include <cstdio>
#include <string>
#include <iomanip>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

#define LL long long
#define pii pair<int,int>
#define sd(x) scanf("%d",&x)
#define slld(x) scanf("%lld",&x)
#define pd(x) printf("%d\n",x)
#define plld(x) printf("%lld\n",x)
#define rep(i,a,b) for(int i = (a) ; i <= (b) ; i++)
#define per(i,a,b) for(int i = (a) ; i >= (b) ; i--)
#define mem(a) memset(a,0,sizeof(a))
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
#define fast_io ios::sync_with_stdio(false)

const LL mod = 1e9 + 7;
const int maxn = 5e5 + 7;
const int INF = 0x3f3f3f3f;
const double pi = acos(-1.0);

LL f[maxn],inv[maxn];

void init() {
    inv[0] = f[0] = inv[1] = f[1] = 1;
    for(LL i = 2 ; i <= maxn ; i++) {
        inv[i] = ((mod - mod / i) * inv[mod%i]) % mod;
        f[i] = i;
    }
    for(LL i = 2 ; i <= maxn ; i++) {
        inv[i] = (inv[i] * inv[i-1]) % mod;
        f[i] = (f[i] * f[i-1]) % mod;
    }
}

LL C(LL x,LL y) {
    return f[x] * inv[y] % mod * inv[x-y] % mod;
}

LL A(LL x,LL y) {
    return f[x] * inv[x-y] % mod;
}

int main() {

#ifndef ONLINE_JUDGE
//	freopen("in.txt", "r", stdin);
//	freopen("out.txt", "w", stdout);
	long _begin_time = clock();
#endif

    int n;
    sd(n);
    LL a, b;
    slld(a), slld(b);
    LL sum = a + b;
    LL Xor = 0;
    rep(i,3,n) {
        LL x;
        slld(x);
        Xor ^= x;
    }

    bool flag = false;
    if(sum < Xor || (sum - Xor) % 2 != 0) flag = true;

    LL And = sum - Xor >> 1;
    LL ans = And;
    per(i,60,0) {
        int xx = ((And >> i) & 1LL);
        int yy = ((Xor >> i) & 1LL);
        if(xx && yy) {
            flag = true;
            break;
        }
        if(!xx && yy && ((ans | (1LL << i)) <= a)) {
            ans |= (1LL << i);
        }
    }

    if(!ans || ans > a || flag) puts("-1");
    else plld(a-ans);

#ifndef ONLINE_JUDGE
	long _end_time = clock();
	// cout << "time = " <<  _end_time - _begin_time << endl;
#endif
    return 0;
}