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: Wrong Answer)

#include <vector>
#include <algorithm>
#include <limits.h>
#include <iostream>
#include <set>
#include <cmath>
#include <queue>
#include <cstring>
#include <string.h>
#include <stdio.h>
#include <iomanip>
#include <map>
#include <unordered_map>
#include <stack>
#define MOD 1000000007
typedef  long long int  lli;
using namespace std;
int main() {
    int t; t=1;
    while(t--) {
      long long int n; cin>>n; long long int a[n];
      for(int i=0;i<n;i++)
      {
          cin>>a[i];
      }
      if(n==2)
      {
          if(a[0]<a[1]){cout<<-1<<"\n";
              continue;}
          else if(a[0]==a[1]){cout<<0<<"\n";
              continue;}
          else if(a[0]>a[1])
          {
              if(((a[0]-a[1])%2)!=0) {cout<<-1<<"\n"; continue;}
              long long int x=(a[0]-a[1])/2;

              cout<<x<<"\n";
              continue;
          }
      }
      long long int X=0;
      for(int i=2;i<n;i++)
      {
          X^=a[i];
      }
      long long int S=a[0]+a[1];
      if((S-X)%2!=0) {cout<<-1<<"\n";
        continue;}

      long long int D=(S-X)/2;
      if(D < 0) {cout<<-1<<"\n";
        continue;}
      if((D&X) != 0){cout<<-1<<"\n";
          continue;}
      if(D>a[0]){cout<<-1<<"\n";
          continue;}
      long long int a_val=D; long long int y=0;
      for(int i=60;i>=0;i--)
      {
          if((X>>i)&1)
          {
              long long int z = y+(1ll<<i);
              if(z+a_val<=a[0])
              {
                  y=z;
              }
          }
      }

      cout<<a[0]-(y+a_val)<<"\n";






        }
    return 0;
}