#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#define N 600000
using namespace std;
const long long inf=(long long)(3e14);
long long read()
{
	char c=0;
	long long sum=0;
	while (c<'0'||c>'9') c=getchar();
	while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
	return sum;
}
struct reads
{
	long long l,r;
	int sz;
};
reads tong[N+1];
struct rds
{
	long long num;
	int data;
	bool operator < (const rds &t)const
	{
		return num<t.num;	
	}
};
rds st[N+1];
int T,n,l,r,length,leng,a[N+1];
long long m,ans;
long long get_rk(long long l,long long r,long long d,long long k)
{
	return l+(k+d-1)/d-1;
}
long long calc(long long l1,long long r1,int d1,long long l2,long long r2,int d2)
{
	if (d1>=d2) return l1+r2;
	else
	{
		if ((r1-l1+1)*d1>=(r2-l2+1)*d2) return get_rk(l1,r1,d1,(r2-l2+1)*d2)+l2;
		else return r1+get_rk(l2,r2,d2,(r2-l2+1)*d2-(r1-l1)*d1);
	}
}
bool check(long long x)
{
	int rst=0,d,ds;
	long long ps,dst=m<<1,res=0,tres=0;
	leng=0,length=1;
	for (int i=1;i<=n;++i) st[++leng]=(rds){a[i],1},st[++leng]=(rds){a[i],1},st[++leng]=(rds){a[i]+(x>>1),-1},st[++leng]=(rds){a[i]+((x+1)>>1),-1},tres+=x;
	if (tres<dst) return 0;
	sort(st+1,st+leng+1);
	for (int i=1;i<=leng;++i)
	{
		rst+=st[i].data;
		if (rst&&dst&&st[i].num!=st[i+1].num)
		{
			d=min(dst/rst,st[i+1].num-st[i].num),dst-=rst*d;
			if (d) tong[++length]=(reads){st[i].num,st[i].num+d-1,rst};
			if (dst&&d!=st[i+1].num-st[i].num) tong[++length]=(reads){st[i].num+d,st[i].num+d,(int)(dst)},dst=0;
		}
	}
	vector<int>p;
	for (int i=1;i<=length;++i)
		for (int j=tong[i].l;j<=tong[i].r;++j)
			for (int k=1;k<=tong[i].sz;++k)
				p.push_back(j);
	l=2,r=length;
	while (l<=r)
	{
		d=min((tong[l].r-tong[l].l+1)*tong[l].sz,(tong[r].r-tong[r].l+1)*tong[r].sz),res=max(res,calc(tong[l].l,tong[l].r,tong[l].sz,tong[r].l,tong[r].r,tong[r].sz));
		if (d==(tong[l].r-tong[l].l+1)*tong[l].sz&&d==(tong[r].r-tong[r].l+1)*tong[r].sz) l++,r--;
		else if (d==(tong[l].r-tong[l].l+1)*tong[l].sz)
		{
			l++,tong[r].r-=(d+tong[r].sz-1)/tong[r].sz,ds=(tong[r].sz-d%tong[r].sz)%tong[r].sz,ps=tong[r].r+1;
			if (tong[r].l>tong[r].r) r--;
			if (ds) tong[++r]=(reads){ps,ps,ds};
		}
		else
		{
			r--,tong[l].l+=(d+tong[l].sz-1)/tong[l].sz,ds=(tong[l].sz-d%tong[l].sz)%tong[l].sz,ps=tong[l].l-1;
			if (tong[l].l>tong[l].r) l++;
			if (ds) tong[--l]=(reads){ps,ps,ds};
		}
	}
	return res+2<=x;
}
int main()
{
	T=read();
	while (T--)
	{
		n=read(),m=read(),ans=0;
		for (int i=1;i<=n;++i) a[i]=read();
		sort(a+1,a+n+1);
		for (int i=log(inf)/log(2);i>=0;--i)
			if (ans+(1ll<<i)<=inf&&!check(ans+(1ll<<i)))
				ans+=(1ll<<i);
		printf("%lld\n",ans+1);
	}
	return 0;
}