#include<bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,j,k) for(int i=(j);i<=(k);i++)
#define per(i,j,k) for(int i=(j);i>=(k);i--)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
typedef vector<int> vi;
typedef pair<int,int> pi;

const int inf=1e18;
void solve(){
	int n,m; cin>>n>>m;
	vi a(n),b(n);
	rep(i,0,n-1){
		cin>>a[i];
	}
	auto chk=[&](int mid){
		auto cchk=[&]()->int{
			vector< array<int,2> > msg;
			rep(i,0,n-1){
				msg.pb({1+a[i],1});
				msg.pb({b[i]+a[i]+1,-1});
				msg.pb({b[i]+1-a[i]-1,2});
				msg.pb({mid-a[i]+1-1,-2});
			}
			sort(msg.begin(),msg.end());
			int res=0,rst=0,ls=-inf;
			int cnt0=0,cnt1=0;
			for(auto x:msg){
				int t=x[0]-ls;
				res+=t*min(cnt0,cnt1);
				int nxt=max(0ll, rst+(cnt0-cnt1)*t );
				if(nxt<rst){
					res+=rst-nxt;
				}
				rst=nxt,ls=x[0];
				if(x[1]==1){
					cnt0++;
				}
				else if(x[1]==-1){
					cnt0--;
				}
				else if(x[1]==2){
					cnt1++;
				}
				else{
					cnt1--;
				}
			}
			return res>=m;
		};
		auto dfs=[&](auto self,int d)->int{
			if(d==n){
				if(cchk()){
					return 1;
				}
				return 0;
			}
			rep(x,mid/2,(mid+1)/2){
				b[d]=x;
				if(self(self,d+1)){
					return 1;
				}
			}
			return 0;
		};
		return dfs(dfs,0);
	};
	int l=0,r=(*max_element(a.begin(),a.end())+m/n+1)*2;
	while(l<r){
		int mid=(l+r)/2;
		if(chk(mid)){
			r=mid;
		}
		else{
			l=mid+1;
		}
	}
	cout<<l<<'\n';
}
signed main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	
	int t; cin>>t;
	while(t--){
		solve();
	}
}