#include <bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define db double
#define inf 0x3f3f3f3f
using namespace std;

const int N=5e5+10,mod=1e9+7;

int main(){
	int n;
	ll a,b,c=0;
	cin>>n>>a>>b;
	for(int i=3;i<=n;i++) {
		ll x;
		cin>>x;
		c^=x;
	}
	ll s=a+b,d=s-c,ans=d/2;
	bool f=true;
	if((d&1)||d<0||ans>a||(ans&c)) f=false;
	if (f) {
		for(ll i=(1ll<<61);i;i>>=1) {
			if((i&c)&&ans+i<=a) 
				ans+=i;
		} 
		if(ans) cout<<a-ans<<endl;
		else cout<<-1<<endl;
	}
	else {
		cout<<-1<<endl;
	}
	
}
### Prompt

Generate a CPP solution to the following problem:

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.

Examples

Input

2
5 3


Output

1


Input

2
3 5


Output

-1


Input

3
1 1 2


Output

-1


Input

8
10 9 8 7 6 5 4 3


Output

3


Input

3
4294967297 8589934593 12884901890


Output

1

### Response

```cpp
#include <bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define db double
#define inf 0x3f3f3f3f
using namespace std;

const int N=5e5+10,mod=1e9+7;

int main(){
	int n;
	ll a,b,c=0;
	cin>>n>>a>>b;
	for(int i=3;i<=n;i++) {
		ll x;
		cin>>x;
		c^=x;
	}
	ll s=a+b,d=s-c,ans=d/2;
	bool f=true;
	if((d&1)||d<0||ans>a||(ans&c)) f=false;
	if (f) {
		for(ll i=(1ll<<61);i;i>>=1) {
			if((i&c)&&ans+i<=a) 
				ans+=i;
		} 
		if(ans) cout<<a-ans<<endl;
		else cout<<-1<<endl;
	}
	else {
		cout<<-1<<endl;
	}
	
}
```