// library begin: "lib/template.hpp"
#ifdef TEMPLATE
#else
#define TEMPLATE
//see https://github.com/ryoku1020/lib
# pragma GCC optimize("O3")
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <cmath>
#include <climits>
#include <cassert>
#include <functional>
#include <iterator>
#include <utility>
#include <complex>
#include <bitset>
#include <chrono>
#include <random>
#include <limits>
#include <optional>
#include <variant>
#include <any>

#include <array>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>
#include <string_view>
#include <tuple>
#include <type_traits>
#include <version>
using namespace std;
namespace ryoku{}
using uint=unsigned;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using i128=__int128;
using u128=unsigned __int128;
template<class T>using vc=vector<T>;
template<class T>using vvc=vc<vc<T>>;
template<class T>using vvvc=vvc<vc<T>>;
template<class T>using smpq=priority_queue<T,vector<T>,greater<T>>;
template<class T>using bipq=priority_queue<T>;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,j,n) for(ll i=(j);i<(ll)(n);i++)
#define DREP(i,n,m) for(ll i=(n);i>=(m);i--)
#define drep(i,n) for(ll i=((n)-1);i>=0;i--)
#define rall(x) x.rbegin(),x.rend()
#define mp(...) make_pair(__VA_ARGS__)
#define pb push_back
#define fi first
#define se second
#define is insert
#define bg begin()
#define ed end()
#define all(x) x.begin(),x.end()
void scan(int&a) { cin >> a; }
void scan(ll&a) { cin >> a; }
void scan(string&a) { cin >> a; }
void scan(char&a) { cin >> a; }
void scan(uint&a) { cin >> a; }
void scan(ull&a) { cin >> a; }
void scan(bool&a) { cin >> a; }
void scan(ld&a){ cin>> a;}
template<class T> void scan(vector<T>&a) { for(auto&x:a) scan(x); }
void read() {}
template<class Head, class... Tail> void read(Head&head, Tail&... tail) { scan(head); read(tail...); }
#define INT(...) int __VA_ARGS__; read(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; read(__VA_ARGS__);
#define ULL(...) ull __VA_ARGS__; read(__VA_ARGS__);
#define STR(...) string __VA_ARGS__; read(__VA_ARGS__);
#define VC(type, name, ...) vector<type> name(__VA_ARGS__); read(name);
#define VVC(type, name, size, ...) vector<vector<type>> name(size, vector<type>(__VA_ARGS__)); read(name);
template<class T>void print(T a) { cout << a; }
template<class T> void print(vector<T>a) { for(int i=0;i<(int)a.size();i++){if(i)cout<<" ";print(a[i]);}}
void PRT() { cout <<endl; return ; }
template<class T> void PRT(T a) { print(a); cout <<endl; return; }
template<class Head, class... Tail> void PRT(Head head, Tail ... tail) { print(head); cout << " "; PRT(tail...); return; }
template<class T,class F>
bool chmin(T &x, F y){
    if(x>y){
        x=y;
        return true;
    }
    return false;
}
template<class T, class F>
bool chmax(T &x, F y){
    if(x<y){
        x=y;
        return true;
    }
    return false;
}
template<typename T>
T floor(T a,T b){
    return a/b-(a%b&&((a<0)!=(b<0)));
}
template<typename T>
T ceil(T a,T b){
    return a/b+(a%b&&((a<0)==(b<0)));
}
template<typename T>
T bmod(T x,T y){
    return x-y*floor(x,y);
}
template<typename T>
pair<T,T>divmod(T x,T y){
    T q=floor(x,y);
    return{q,x-q*y};
}
void YesNo(bool b){
    cout<<(b?"Yes":"No")<<endl;
}
void YESNO(bool b){
    cout<<(b?"YES":"NO")<<endl;
}
void AliceBob(bool b){
    cout<<(b?"Alice":"Bob")<<endl;
}
void TakahashiAoki(bool b){
    cout<<(b?"Takahashi":"Aoki")<<endl;
}
void Yes(){
    cout<<"Yes"<<endl;
}
void No(){
    cout<<"No"<<endl;
}
vc<int>stovi(const string&s,const string&S){
    vc<int>v(s.size());
    rep(i,s.size()){
        auto t=S.find(s[i]);
        assert(t!=string::npos);
        v[i]=t;
    }
    return v;
}
template<class T=ll>
T isqrt(T x){
    T F=sqrtl(x);
    while((F+1)*(F+1)<=x)F++;
    while(F*F>x)F--;
    return F;
}
template<class T>
T tri(T x){return x*(x-1)/2;}

//[l,r)
template<class T>T tri(T l,T r){return (r-l)*(l+r-1)/2;}
//n を先頭に持ってくる
template<class T>
vc<T>rot(vc<T>v,int n){
    rotate(v.begin(),v.begin()+n,v.end());
    return v;
}
template<class Container>
auto rle(const Container&cv){
    using T=typename Container::value_type;
    vc<pair<T,int>>res;
    for(const auto&x:cv){
        if(res.empty()||res.back().fi!=x)res.pb({x,1});
        else res.back().se++;
    }
    return res;
}
template<class T>
vc<T>iota(int n){
    vc<T>v(n);rep(i,n)v[i]=i;
    return v;
}
template<class T,int minfirst>
vc<int>argsort(const vc<T>&a){
    auto idx=iota<int>(a.size());
    sort(all(idx),[&](int i,int j){
        return (minfirst?make_pair(a[i],i)<make_pair(a[j],j):make_pair(a[i],i)>make_pair(a[j],j));
    });
    return idx;
}
template<class T>
vvc<T>trans(const vvc<T>&a){
    assert(a.size()&&a[0].size());
    rep(i,a.size())assert(a[i].size()==a[0].size());
    vvc<T>b(a[0].size(),vc<T>(a.size()));
    rep(i,a.size())rep(j,a[0].size())b[j][i]=a[i][j];
    return b;
}
vc<string>trans(const vc<string>&a){
    assert(a.size()&&a[0].size());
    rep(i,a.size())assert(a[i].size()==a[0].size());
    vc<string>b(a[0].size(),string(a.size(),0));
    rep(i,a.size())rep(j,a[0].size())b[j][i]=a[i][j];
    return b;
}
template<class T>
int popcount(T n){
    return __builtin_popcountll(n);
}
template<class T,class L=ll>
L sum(const vc<T>&a){
    return accumulate(all(a),L(0));
}
template<class T>
struct subset_view{
    T s;
    struct iterator{
        T s,x;
        bool done;
        T operator*()const{return x;}
        iterator&operator++(){
            if(x==0)done=true;
            else x=(x-1)&s;
            return*this;
        }
        bool operator!=(const iterator&r)const{return done!=r.done;}
    };
    iterator begin()const{return{s,s,false};}
    iterator end()const{return{s,0,true};}
};
template<class T>
subset_view<T>subset(T s){
    return{s};
}
template<class T>
T max(vc<T>&a){
    return *max_element(all(a));
}
template<class T>
T min(vc<T>&a){
    return *min_element(all(a));
}
template<class T,class L=ll>
vc<L> presum(vc<T> &a){
    vc<L> ret(a.size()+1);
    rep(i,a.size())ret[i+1]=ret[i]+a[i];
    return ret;
}
template<class T, class F>
vc<T> &operator+=(vc<T> &a,F b){
    for (auto&v:a)v += b;
    return a;
}
template<class T, class F>
vc<T> &operator-=(vc<T>&a,F b){
    for (auto&v:a)v-=b;
    return a;
}
template<class T, class F>
vc<T> &operator*=(vc<T>&a,F b){
    for (auto&v:a)v*=b;
    return a;
}
template<class T=ll>
constexpr T pow(T a,T b){
    T res=1;
    while(b){
        if(b&1)res*=a;
        a*=a;
        b/=2;
    }
    return res;
}
constexpr ll ten(ll a){
    return pow<ll>(10,a);
}
template<typename T>constexpr T inf=numeric_limits<T>::max()/2-1;
template<>
constexpr pll inf<pll> ={inf<ll>,inf<ll>};
template<class T>
constexpr T neg_inf=-inf<T>;
template<>
constexpr pll neg_inf<pll> ={-inf<ll>,-inf<ll>};
template<class T>
int tbit(T x){
    using U=make_unsigned_t<T>;
    U y=(U)x;
    return y?(int)bit_width(y)-1:-1;
}
template<class T>
int lbit(T x){
    using U=make_unsigned_t<T>;
    U y=(U)x;
    return y?(int)countr_zero(y):-1;
}
template<class T>
int tbit(T x,int p){
    using U=make_unsigned_t<T>;
    constexpr int W=numeric_limits<U>::digits;
    U y=(U)x;
    if(p<0)return -1;
    if(p>=W-1)return tbit(y);
    return tbit(y&((U(1)<<(p+1))-1));
}
template<class T>
int lbit(T x,int p){
    using U=make_unsigned_t<T>;
    constexpr int W=numeric_limits<U>::digits;
    U y=(U)x;
    if(p<0)return lbit(y);
    if(p>=W)return -1;
    return lbit(y&(~U(0)<<p));
}
istream& operator>>(istream&is,i128&x){
    string s;is>>s;
    x=0;
    int i=0,neg=0;
    if(s[0]=='-')neg=1,i=1;
    for(;i<(int)s.size();i++)x=x*10+s[i]-'0';
    if(neg)x=-x;
    return is;
}
ostream& operator<<(ostream&os,i128 x){
    if(x==0)return os<<0;
    if(x<0)os<<"-";
    u128 y=x<0?-(u128)x:(u128)x;
    string s;
    while(y)s.pb('0'+y%10),y/=10;
    reverse(all(s));
    return os<<s;
}
#ifdef LOCAL
#include"lib/debug/local.hpp"
inline int dbging=1;
#else
#define dbg(...) ((void)0)
#endif

struct template_setup{
    template_setup(){
        #if defined(LOCAL)&&!defined(INTERACTIVE)
        freopen("input.txt","r",stdin);
        freopen("output.txt","w",stdout);
        
        #endif
        cin.tie(0)->sync_with_stdio(0);
        #ifdef LOCAL
        cout<<fixed<<setprecision(6);
        #else
        cout<<fixed<<setprecision(20);
        #endif
    }
};
inline template_setup template_setup;


#endif
// library end: "lib/template.hpp"
// library begin: "lib/math/number_theory/extgcd-asexp.hpp"
// library include: "lib/template.hpp"
// library begin: "lib/math/modular/mod-utillity.hpp"

// library include: "lib/template.hpp"
// library begin: "lib/math/modular/dynamic-mod-int.hpp"
// library include: "lib/template.hpp"
// library begin: "lib/math/modular/barrett.hpp"
// library include: "lib/template.hpp"
namespace ryoku{
struct barrett{
    using u64=uint64_t;
    using u32=uint32_t;
    using i128=__int128_t;
    u64 m;
    int mod;
    void set(int mod_){
        assert(mod_>0);
        mod=mod_;
        m=(i128(1)<<64)/mod;
    }
    unsigned reduce(uint64_t x){
        assert(mod>0);
        x-=(((i128)x*m)>>64)*mod;
        return x<mod?x:x-mod;
    }
};

}
// library end: "lib/math/modular/barrett.hpp"
namespace ryoku{
template<int id>
struct dynamic_modint{
    using u32=uint32_t;
    using u64=uint64_t;
    u32 val;
    dynamic_modint():val(0){}
    dynamic_modint(ll x){
        ll v=x%get_mod();
        if(v<0)v+=get_mod();
        val=v;
    }
    static dynamic_modint raw(int v){
        assert(v>=0);
        dynamic_modint mi;
        mi.val=v;
        return mi;
    }
    dynamic_modint &operator+=(const dynamic_modint&m){
        u32 md=get_mod();
        u32 x=val+m.val-md;
        val=x+(md&-(x>>31));
        return *this;
    }
    dynamic_modint &operator-=(const dynamic_modint&m){
        u32 md=get_mod();
        u32 x=val-m.val;
        val=x+(md&-(x>>31));
        return *this;
    }
    dynamic_modint &operator*=(const dynamic_modint&m){
        val=rem(u64(val)*m.val);
        return *this;
    }
    dynamic_modint &operator/=(const dynamic_modint&m){
        val=rem(u64(val)*m.inv().val);
        return *this;
    }
    dynamic_modint operator-() const{
        return dynamic_modint(val?get_mod()-val:0);
    }
    dynamic_modint operator+() const {
        return *this;
    }
    friend dynamic_modint operator+(dynamic_modint lhs, const dynamic_modint& rhs){
        return lhs+=rhs;
    }
    friend dynamic_modint operator-(dynamic_modint lhs, const dynamic_modint& rhs){
        return lhs-=rhs;
    }
    friend dynamic_modint operator*(dynamic_modint lhs, const dynamic_modint& rhs){
        return lhs*=rhs;
    }
    friend dynamic_modint operator/(dynamic_modint lhs,const dynamic_modint&rhs){
        return lhs/=rhs;
    }
    bool operator==(const dynamic_modint&p) const{
        return p.val==val;
    }
    bool operator!=(const dynamic_modint&p) const{
        return p.val!=val;
    }
    dynamic_modint pow(int64_t n) const{
        dynamic_modint res(1),mul(val);
        while(n){
            if(n%2)res*=mul;
            mul*=mul;
            n/=2;
        }
        return res;
    }

    friend ostream&operator<<(ostream&os,const dynamic_modint&p){
        os<<p.val;
        return os;
    }
    friend istream&operator>>(istream&is,dynamic_modint&p){
        int64_t x;
        is>>x;
        p=dynamic_modint(x);
        return is;
    }
    dynamic_modint inv()const{
        int64_t a=val,b=get_mod(),u=1,v=0,t;
        #ifdef LOCAL
        assert(gcd(a,b)==1);
        #endif
        while(b>0){
            t=a/b;
            swap(a-=t*b,b);
            swap(u-=t*v,v);
        }
        return dynamic_modint(u);
    }
    inline static u32 rem(u64 x){return barrett_reduction().reduce(x);}
    static inline int &get_mod(){
        static int mod=0;
        return mod;
    }
    static void set_mod(int md){
        assert(0<md&&md<=(1ll<<31)-1);
        get_mod()=md;
        barrett_reduction().set(md);
    }
    static inline barrett&barrett_reduction(){
        static barrett b;
        return b;
    }
};

}
// library end: "lib/math/modular/dynamic-mod-int.hpp"

namespace ryoku{
template<typename T>
T extgcd(T a,T b,T &x,T &y){
    T d=a;
    if(b!=0){
        d=extgcd(b,a%b,y,x);
        y-=(a/b)*x;
    }else{
        x=(a>=0?1:-1);
        y=0;
        d=(a>=0?a:-a);
    }
    return d;
}
template<class T>
pair<T,T> inv(T x,T m){
    T a1,a2;
    T res=extgcd<ll>(x,m,a1,a2);
    T md=m/res;
    a1=(a1%md+md)%md;
    return {a1,md};
}
template<class T>
pair<T,T> mod_solve(T a,T b,T m){//return x s.t. ax=b mod m
    a%=m,b%=m;if(a<0)a+=m;if(b<0)b+=m;
    T g=gcd(gcd(a,b),m);
    a/=g,b/=g,m/=g;
    if(gcd(a,m)>1)return {-1,-1};
    return {(inv<ll>(a,m).first*b)%m,inv<ll>(a,m).second};
}

//x^2 ≡ b (mod p)
ll mod_sqrt(ll b,ll p){
    static mt19937 mt(random_device{}());
    b%=p;if(b<0)b+=p;
    if(b==0)return 0;
    if(p==2){
        return b;
    }
    assert(p>=3);
    using mint=dynamic_modint<20260801>;mint::set_mod(p);
    if(mint(b).pow((p-1)/2)==-1){
        return -1;
    }
    if(p%4==3){
        return mint(b).pow((p+1)/4).val;
    }
    ll t=[&](){
        ll w;
        while(1){
            ll t=mt()%p;
            w=t*t-b;
            if(mint(w).pow((p-1)/2)==mint(-1)){
                return t;
            }
        }
        assert(0);
    }();
    mint w=mint(t*t-b);
    using T=pair<mint,mint>;
    auto ml=[&](T a,T b)->T{
        return T{a.first*b.first+a.second*b.second*w,a.second*b.first+a.first*b.second};
    };
    ll e=(p+1)/2;
    T ans={1,0};
    T gy={t,1};
    while(e){
        if(e%2)ans=ml(ans,gy);
        gy=ml(gy,gy);
        e/=2;
    }
    return ans.first.val;
}

}
// library end: "lib/math/modular/mod-utillity.hpp"
namespace ryoku{

//ax+by=c
//res.fi.fi*t+res.fi.se, res.se.fi*t+res.se.se という解集合
template<class T>
pair<pair<T,T>,pair<T,T>>extgcdasexp(T a,T b,T c){
    T g=gcd(a,b);
    assert(a||b);
    if(c%g)return {{-inf<T>,-inf<T>},{-inf<T>,-inf<T>}};
    c/=g,a/=g,b/=g;
    T x,y;
    extgcd(a,b,x,y);
    x*=c,y*=c;
    return {{-b,x},{a,y}};
}
}
// library end: "lib/math/number_theory/extgcd-asexp.hpp"
// library begin: "lib/math/number_theory/valid-segment.hpp"
// library include: "lib/template.hpp"
//at+b \in [l,r] なる t の閉区間
namespace ryoku{
template<class T>
pair<T,T>validsegment(T a,T b,T l,T r){
    if(a==0){
        if(l<=b&&b<=r)return {-inf<T>,inf<T>};
        return {0,-1};
    }
    if(a>0){
        return {ceil<T>(l-b,a),floor<T>(r-b,a)};
    }else{
        return {ceil<T>(r-b,a),floor<T>(l-b,a)};
    }
}
}
// library end: "lib/math/number_theory/valid-segment.hpp"
using namespace ryoku;
void solve(){
    LL(m,a,b,k);
    //[0,m)  
    auto solve=[&](auto&solve,ll m,ll a,ll b,ll k)->ll{
        ll L=lcm(a,b);
        if(m>L){
            ll ans=solve(solve,L,a,b,k)*(m/L)+solve(solve,m%L,a,b,k);
            dbg(m%L);
            dbg(ans);
            if(a==k){
                ans+=m/L;
            }
            return ans;
        }
        assert(m<=L);
        if(m<a)return 0;
        if(a<k){
            return 0;
        }
        if(a==k){
            ll MA=(m-1)/a*a;
            ll MB=(m-1)/b*b;
            ll res=((m-1)/a)-(m-1)/b;
            if(MA<MB)res+=1;
            dbg(m,a,b,k,res);
            return res;
        }
        assert(a>k);
        ll ans=0;
        auto work=[&](ll a,ll b){
            dbg("========="s);
            auto P=extgcdasexp(a,-b,k);
            dbg(a,-b,k);
            dbg(P.fi,P.se);
            auto alr=validsegment<ll>(P.fi.fi*a,P.fi.se*a,0,m-1);
            auto blr=validsegment<ll>(P.se.fi*b,P.se.se*b,0,m-1);
            ll L=max(alr.fi,blr.fi);
            ll R=min(alr.se,blr.se);
            dbg(alr,blr);
            dbg(a,b,L,R,m,k);
            ans+=max(R-L+1,0ll);
        };
        work(a,b);
        work(b,a);
        dbg(m,a,b,k,ans);
        return ans;
    };
    ll res=solve(solve,m+1,a,b,k);
    if(a==k&&m>=a)--res;
    PRT(res);
}
signed main(){
    int t=1;
     cin >> t;
    while(t--)solve();
}