Problem:
Score : 400 points

Problem Statement

There are N mountains in a circle, called Mountain 1, Mountain 2, ..., Mountain N in clockwise order. N is an odd number.

Between these mountains, there are N dams, called Dam 1, Dam 2, ..., Dam N. Dam i (1 \leq i \leq N) is located between Mountain i and i+1 (Mountain N+1 is Mountain 1).

When Mountain i (1 \leq i \leq N) receives 2x liters of rain, Dam i-1 and Dam i each accumulates x liters of water (Dam 0 is Dam N).

One day, each of the mountains received a non-negative even number of liters of rain.

As a result, Dam i (1 \leq i \leq N) accumulated a total of A_i liters of water.

Find the amount of rain each of the mountains received. We can prove that the solution is unique under the constraints of this problem.

Constraints

All values in input are integers.

3 \leq N \leq 10^5-1

N is an odd number.

0 \leq A_i \leq 10^9

The situation represented by input can occur when each of the mountains receives a non-negative even number of liters of rain.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print N integers representing the number of liters of rain Mountain 1, Mountain 2, ..., Mountain N received, in this order.

Sample Input 1

3
2 2 4

Sample Output 1

4 0 4

If we assume Mountain 1, 2, and 3 received 4, 0, and 4 liters of rain, respectively, it is consistent with this input, as follows:

Dam 1 should have accumulated \frac{4}{2} + \frac{0}{2} = 2 liters of water.

Dam 2 should have accumulated \frac{0}{2} + \frac{4}{2} = 2 liters of water.

Dam 3 should have accumulated \frac{4}{2} + \frac{4}{2} = 4 liters of water.

Sample Input 2

5
3 8 7 5 5

Sample Output 2

2 4 12 2 8

Sample Input 3

3
1000000000 1000000000 0

Sample Output 3

0 2000000000 0

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define rg register
#define rep(i,a,b) for (rg int i=a;i<=b;i++)
#define per(i,a,b) for (rg int i=b;i>=a;i--)
#define pb push_back
#define lowbit(x) (x&(-x))
#define mk make_pair
#define VI vector<int>
#define pii pair<int,int>
#define pLL pair<long long,long long>
#define fi first
#define se second
#define il inline
#define ll long long
#define db double
#define ld long double
#define inf 0x3f3f3f3f
#define getc() (p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<15,stdin),p1==p2)?EOF:*p1++)
char buf[1<<15],*p1 = buf,*p2 = buf;
inline ll read(){
    #define num ch-'0'
    char ch;bool flag=0;ll res;
    while(!isdigit(ch=getc()))
    (ch=='-')&&(flag=true);
    for(res=num;isdigit(ch=getc());res=res*10ll+num);
    (flag)&&(res=-res);
    #undef num
    return res;
}
inline void write(ll x){
	if (x < 0) x = ~x + 1ll, putchar('-');
	if (x > 9) write(x / 10ll);
	putchar(x % 10ll + '0');
}
#define mid ((l + r)>>1)
#define ls (x<<1)
#define rs ((x<<1)|1)
#undef mid
#undef ls
#undef rs
#define maxn 101000
int a[maxn];
int b[maxn];
int n;
int check(int v)
{
	b[1] = v;
	rep(i,1,n-1)
	{
		b[i+1] = a[i] - b[i];
		if(b[i]<0)
		{
			if(i%2 == 1) return 1;
			else return -1;
		}
	}
	if(b[n]+b[1] < a[n]) return 1;
	else if(b[n]+b[1]>a[n]) return  -1;
	return 0;
}
void solve()
{
	n = read();
	rep(i,1,n) a[i] = read();
	int l = 0,r = a[1];
	int ans = 0;
	while(l<=r)
	{
		int mid = (l+r)>>1;
		int t = check(mid);
		if(t == 0) break;
		if(t == 1) l = mid+1;
		else r = mid - 1;
	}
	rep(i,1,n) cout<<b[i]*2<<" ";
}
int main()
{
	#ifndef ONLINE_JUDGE
	freopen("data.txt","r",stdin);
	#endif
//	int T = read();
//	while(T--)
	solve();
}