Problem: Snuke has X+Y balls. X of them have an integer A written on them, and the other Y of them have an integer B written on them.

Snuke will divide these balls into some number of groups. Here, every ball should be contained in exactly one group, and every group should contain one or more balls.

A group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C. Find the maximum possible number of good groups.

Solve T test cases for each input file.

Constraints

* 1 \leq T \leq 2 \times 10^4
* 1 \leq A,X,B,Y,C \leq 10^9
* A \neq B

Input

Input is given from Standard Input in the following format. The first line is as follows:


T


Then, T test cases follow. Each test case is given in the following format:


A X B Y C


Output

For each test case, print a line containing the maximum possible number of good groups.

Example

Input

3
3 3 4 4 5
2 1 1 5 3
3 1 4 2 5


Output

2
2
0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

template<class t>
void print(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
}
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif
	return uniform_int_distribution<ll>(l, r)(gen);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

int gcd(int a,int b){return b?gcd(b,a%b):a;}

template<class t=ll>
t extgcd(t a,t b,t&x,t&y){
	if(b==0){
		x=1;
		y=0;
		return a;
	}else{
		t g=extgcd(b,a%b,y,x);
		y-=a/b*x;
		return g;
	}
}

//x*y=g mod m
//returns (g,y)
template<class t=ll>
pair<t,t> modinv(t x,t m){
	t a,b;
	t g=extgcd(x,m,a,b);
	if(a<0)a+=m/g;
	return {g,a};
}

int fdiv(int a,int b){
	return a/b-(a%b&&(a^b)<0);
}

void slv(){
	int a,x,b,y,c;
	cin>>a>>x>>b>>y>>c;
	{
		int g=gcd(a,b);
		a/=g;
		b/=g;
		c/=gcd(g,c);
	}
	rep(_,2){
		int g=gcd(a,c);
		a/=g;
		c/=g;
		int h=gcd(b,g);
		b/=h;
		y/=g/h;
		
		swap(a,b);
		swap(x,y);
	}
	if(c==1){
		print(x+y);
		return;
	}
	int step=modinv(b,c).b*a%c;
	vi pos,cnt;
	{
		int z=modinv(step,c).b;
		int h=step;
		int w=c;
		int cur=0;
		while(w){
			int p=w/h;
			pos.pb(cur*z%c);
			cnt.pb(p);
			cur+=p*h;
			w%=h;
			if(w==0)break;
			h%=w;
			if(h==0)h=w;
		}
		assert(cur==c);
		pos.pb(c);
	}
	auto gety=[&](int v){
		if(v==0)return c;
		return (c-step*v%c)%c;
	};
	int ans=0;
	rep(i,si(cnt)){
		int lx=pos[i],ly=gety(lx);
		int rx=pos[i+1],ry=gety(rx);
		int dx=(rx-lx)/cnt[i];
		int dy=(ly-ry)/cnt[i];
		int lw=0,up=x+y+1;
		while(up-lw>1){
			const int mid=(lw+up)/2;
			int p=fdiv(x-lx*mid,dx);
			int q=fdiv(y-ry*mid,dy);
			if(p>=0&&q>=0&&p+q>=cnt[i]*mid)
				lw=mid;
			else
				up=mid;
		}
		chmax(ans,lw);
	}
	print(ans);
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	int t;cin>>t;
	rep(_,t)slv();
}