#include "dzilib.h"
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef basic_string<int> BI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937_64 mrand(114514); 
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head

typedef pair<ll,ll> PLL;
namespace Factor {
	const int N=1010000;
	ll C,fac[10010],n,mut,a[1001000];
	int T,cnt,i,l,prime[N],p[N],psize,_cnt;
	ll _e[100],_pr[100];
	vector<ll> d;
	inline ll mul(ll a,ll b,ll p) {
		if (p<=1000000000) return a*b%p;
		else if (p<=1000000000000ll) return (((a*(b>>20)%p)<<20)+(a*(b&((1<<20)-1))))%p;
		else {
			ll d=(ll)floor(a*(long double)b/p+0.5);
			ll ret=(a*b-d*p)%p;
			if (ret<0) ret+=p;
			return ret;
		}
	}
	void prime_table(){
		int i,j,tot,t1;
		for (i=1;i<=psize;i++) p[i]=i;
		for (i=2,tot=0;i<=psize;i++){
			if (p[i]==i) prime[++tot]=i;
			for (j=1;j<=tot && (t1=prime[j]*i)<=psize;j++){
				p[t1]=prime[j];
				if (i%prime[j]==0) break;
			}
		}
	}
	void init(int ps) {
		psize=ps;
		prime_table();
	}
	ll powl(ll a,ll n,ll p) {
		ll ans=1;
		for (;n;n>>=1) {
			if (n&1) ans=mul(ans,a,p);
			a=mul(a,a,p);
		}
		return ans;
	}
	bool witness(ll a,ll n) {
		int t=0;
		ll u=n-1;
		for (;~u&1;u>>=1) t++;
		ll x=powl(a,u,n),_x=0;
		for (;t;t--) {
			_x=mul(x,x,n);
			if (_x==1 && x!=1 && x!=n-1) return 1;
			x=_x;
		}
		return _x!=1;
	}
	bool miller(ll n) {
		if (n<2) return 0;
		if (n<=psize) return p[n]==n;
		if (~n&1) return 0;
		for (int j=0;j<=7;j++) if (witness(rand()%(n-1)+1,n)) return 0;
		return 1;
	}
	ll gcd(ll a,ll b) {
		ll ret=1;
		while (a!=0) {
			if ((~a&1) && (~b&1)) ret<<=1,a>>=1,b>>=1;
			else if (~a&1) a>>=1; else if (~b&1) b>>=1;
			else {
				if (a<b) swap(a,b);
				a-=b;
			}
		}
		return ret*b;
	}
	ll rho(ll n) {
		for (;;) {
			ll X=rand()%n,Y,Z,T=1,*lY=a,*lX=lY;
			int tmp=20;
			C=rand()%10+3;
			X=mul(X,X,n)+C;*(lY++)=X;lX++;
			Y=mul(X,X,n)+C;*(lY++)=Y;
			for(;X!=Y;) {
				ll t=X-Y+n;
				Z=mul(T,t,n);
				if(Z==0) return gcd(T,n);
				tmp--;
				if (tmp==0) {
					tmp=20;
					Z=gcd(Z,n);
					if (Z!=1 && Z!=n) return Z;
				}
				T=Z;
				Y=*(lY++)=mul(Y,Y,n)+C;
				Y=*(lY++)=mul(Y,Y,n)+C;
				X=*(lX++);
			}
		}
	}
	void _factor(ll n) {
		for (int i=0;i<cnt;i++) {
			if (n%fac[i]==0) n/=fac[i],fac[cnt++]=fac[i];}
		if (n<=psize) {
			for (;n!=1;n/=p[n]) fac[cnt++]=p[n];
			return;
		}
		if (miller(n)) fac[cnt++]=n;
		else {
			ll x=rho(n);
			_factor(x);_factor(n/x);
		}
	}
	void dfs(ll x,int dep) {
		if (dep==_cnt) d.pb(x);
		else {
			dfs(x,dep+1);
			for (int i=1;i<=_e[dep];i++) dfs(x*=_pr[dep],dep+1);
		}
	}
	void norm() {
		sort(fac,fac+cnt);
		_cnt=0;
		rep(i,0,cnt) if (i==0||fac[i]!=fac[i-1]) _pr[_cnt]=fac[i],_e[_cnt++]=1;
			else _e[_cnt-1]++;
	}
	vector<ll> getd() {
		d.clear();
		dfs(1,0);
		return d;
	}
	vector<ll> factor(ll n) {
		cnt=0;
		_factor(n);
		norm();
		return getd();
	}
	vector<PLL> factorG(ll n) {
		cnt=0;
		_factor(n);
		norm();
		vector<PLL> d;
		rep(i,0,_cnt) d.pb(mp(_pr[i],_e[i]));
		return d;
	}
	bool is_primitive(ll a,ll p) {
		assert(miller(p));
		vector<PLL> D=factorG(p-1);
		a%=p;
		if (a<0) a+=p;
		if (a==0) return 0;
		rep(i,0,SZ(D)) if (powl(a,(p-1)/D[i].fi,p)==1) return 0;
		return 1;
	}
	int D(ll x) {
		auto d=factorG(x);
		int v=1;
		for (auto [p,e]:d) v=v*(e+1);
		return v;
	}
}

bool ispr(int x) {
	for (int i=2;i<x;i++) if (x%i==0) {
		return 0;
	}
	return 1;
}

/*
ll ans=-1;
int GetT() {
	return 1000;
}
ll GetN() {
	return 100000000000000ll;
}
int GetQ() {
	return 720;
}
ll GetC() {
	return 100000000000000000ll;
}
int cnt=0;
ll Ask(ll x) {
	if (ans==-1) {
		ans=mrand()%GetN()+1;
	}
	++cnt;
	return Factor::D(ans+x);
}
void Answer(ll x) {
	assert(x==ans);
	ans=-1;
}*/

map<ll,int> cache;
ll offset;
ll myask(ll x) {
	if (cache.count(x)) return cache[x];
	return cache[x]=Ask(x+offset);
}
int mc=0;
void solve() {
	cache.clear();
	offset=mrand()%GetN()+123456;
	ll lim=GetN()+offset;
	ll p2=8,r2=-1;
	int v=0;
	while (1) {
		myask(v);
		vector<ll> pos;
		rep(o,0,p2) {
			bool val=1;
			for (auto [key,d]:cache) {
				int z=(o+key)%p2;
				if (z!=0) {
					val&=d%(__builtin_ctz(z)+1)==0;
				}
			}
			if (val) pos.pb(o);
		}
		if (SZ(pos)==1) {
			r2=pos[0];
			break;
		}
		++v;
	}
	while (p2<=lim) {
		ll o=(p2-r2)%p2;
		while (1) {
			int d=myask(o);
			if (d%(__builtin_ctzll(p2)+1)!=0) {
				p2*=2;
				r2=(p2-o%p2)%p2;
				break;
			}
			ll q2=p2*4;
			vector<ll> pos;
			for (ll cand:{r2,r2+p2,r2+p2*2,r2+p2*3}) {
				bool val=1;
				for (auto [key,d]:cache) {
					int z=(cand+key)%q2;
					if (z!=0) {
						val&=d%(__builtin_ctz(z)+1)==0;
					}
				}
				if (val) pos.pb(cand);
			}
			if (SZ(pos)==1) {
				r2=pos[0];
				p2=q2;
				break;
			}
			o+=p2;
		}
	}
	Answer(r2-offset);
}
int main() {
	Factor::init(1000000);
	for (int _=GetT();_;_--) {
		solve();
	}
}