//Author: Kevin
#include<bits/stdc++.h>
//#pragma GCC optimize("O2")
using namespace std;
#define ll long long
#define ull unsigned ll
#define pb emplace_back
#define mp make_pair
#define ALL(x) (x).begin(),(x).end()
#define rALL(x) (x).rbegin(),(x).rend()
#define srt(x) sort(ALL(x))
#define rev(x) reverse(ALL(x))
#define rsrt(x) sort(rALL(x))
#define sz(x) (int)(x.size())
#define inf 0x3f3f3f3f
#define pii pair<int,int>
#define lb(v,x) (int)(lower_bound(ALL(v),x)-v.begin())
#define ub(v,x) (int)(upper_bound(ALL(v),x)-v.begin())
#define uni(v) v.resize(unique(ALL(v))-v.begin())
#define longer __int128_t
void die(string S){puts(S.c_str());exit(0);}
ll a[100100];
struct block
{
	ll A,B,M;
	block(){}
	block(ll _A,ll _B,ll _M):A(_A),B(_B),M(_M){};
	inline ll length(){return (B-A+1)*M;}
	inline ll lget(ll x){return (x-1)/M+A;};
	inline ll rget(ll x){return lget(length()-x+1);}
	inline ll lgetd(ll x){return (x-1)/M*M+M-(x-1);}
	inline ll rgetd(ll x){return lgetd(x);}
	inline ll lgetd2(ll x){return (x-1)-(x-1)/M*M+1;}
	inline ll rgetd2(ll x){return lgetd2(x);}
};
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int t;
	cin>>t;
	while(t--)
	{
		int n;
		ll m;
		cin>>n>>m;
		for(int i=1;i<=n;i++)
		{
			cin>>a[i];
			a[i]++;
		}
		sort(a+1,a+n+1);
		vector<block> vec;
		for(int i=1;i<n;i++)
			if((a[i+1]-a[i])*i<=m)
			{
				vec.pb(a[i],a[i+1]-1,i);
				m-=(a[i+1]-a[i])*i;
			}
			else
			{
				if(m/i)
					vec.pb(a[i],a[i]+m/i-1,i);
				if(m%i)
					vec.pb(a[i]+m/i,a[i]+m/i,m%i);
				m=0;
			}
		if(m/n)
			vec.pb(a[n],a[n]+m/n-1,n);
		if(m%n)
			vec.pb(a[n]+m/n,a[n]+m/n,m%n);
		ll L=0,R=0;
		int lp=0,rp=sz(vec)-1;
		ll ans=0;
		while(lp<sz(vec))
		{
			if(L==vec[lp].length())
			{
				L=0;
				lp++;
				continue;
			}
			if(R==vec[rp].length())
			{
				R=0;
				rp--;
				continue;
			}
			ll len=min(vec[lp].length()-L,vec[rp].length()-R);
			// ...
			ans=max(ans,vec[lp].lget(L+1)+vec[rp].rget(R+1));
			ans=max(ans,vec[lp].lget(L+len)+vec[rp].rget(R+len));
			if(vec[lp].M>=vec[rp].M)
				if(vec[lp].lgetd(L+1)<vec[rp].rgetd(R+1)&&vec[lp].lgetd(L+1)<=len-1)
					ans=max(ans,vec[lp].lget(L+1)+vec[rp].rget(R+1)+1);
			if(vec[lp].M<=vec[rp].M)
				if(vec[lp].lgetd2(L+len)>vec[rp].rgetd2(R+len)&&vec[rp].rgetd2(R+len)<=len-1)
					ans=max(ans,vec[lp].lget(L+len)+vec[rp].rget(R+len)+1);
			L+=len;
			R+=len;
		}
		if(n==1) ans=max(ans,m+m);
		cout<<ans<<'\n';
	}
	return 0;
}