// what is matter? never mind. 
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2")
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
//#define ull unsigned long long
#define int long long
#define SZ(x) ((int)((x).size()))
#define ALL(x) (x).begin(),(x).end()
using namespace std;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	return f?-x:x;
}

#define mod 998244353
struct modint{
	unsigned int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x<o.x?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,modint b){return a.x==b.x;}
	friend bool operator !=(modint a,modint b){return a.x!=b.x;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define maxn 1000005
#define inf 0x3f3f3f3f

int n,a[maxn];
vector<pii>R[maxn];

void work()
{
	n=read();
	For(i,0,n-1)a[i]=a[i+n]=read();
	For(i,0,n*2) R[i].clear();
	
	R[n*2-1].pb(mkp(a[n*2-1],n*2-1));
	Rep(i,n*2-2,0){
		R[i].pb(mkp(a[i],i));
		for(auto [x,p]:R[i+1]){
			x=x/2+a[i];
			if(x>R[i].back().fi) R[i].pb(mkp(x,p));
		}
	}
	
	vector<pii> L;
	L.pb(mkp(a[0],0));
	For(i,1,n*2-1){
		vector<pii> nL;
		nL.pb(mkp(a[i],i));
		for(auto [x,p]:L){
			x=x/2+a[i];
			if(x>nL.back().fi) nL.pb(mkp(x,p));
		}
		swap(L,nL);
		if(i>=n){
			i-=n;
			int res=0;
			int p=SZ(R[i])-1;
			for(auto [x1,p1]:L){
				while(p>=0){
					auto [x2,p2]=R[i][p];
					int len=(i+n-p1+1)+(p2-i);
					if(len>n) --p;
					else {
						res=max(res,x1+x2-a[i]);
						break;
					}
				}
			}
			cout<<res<<" ";
			i+=n;
		}
	}
	cout<<"\n";
}

signed main()
{
	int T=read();
	while(T--)work();
	return 0;
}
/*

*/