#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db; 
typedef string str; 

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5; 
const ll INF = 1e18; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

template<class T> bool ckmin(T& a, const T& b) { 
	return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
	return a < b ? a = b, 1 : 0; } 
int pct(int x) { return __builtin_popcount(x); } 
int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
//int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0 
int fstTrue(function<bool(int)> f, int lo, int hi) {
	hi ++; assert(lo <= hi); // assuming f is increasing
	while (lo < hi) { // find first index such that f is true 
		int mid = (lo+hi)/2; 
		f(mid) ? hi = mid : lo = mid+1; 
	} 
	return lo;
}

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
template<class A> str ts(complex<A> c) { 
	stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) { 
	str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
	res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
	str res = ""; F0R(i,SZ) res += char('0'+b[i]);
	return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
	bool fst = 1; str res = "{";
	for (const auto& x: v) {
		if (!fst) res += ", ";
		fst = 0; res += ts(x);
	}
	res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
	return "("+ts(p.f)+", "+ts(p.s)+")"; }

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
	pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
	pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
	cerr << ts(h); if (sizeof...(t)) cerr << ", ";
	DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif

// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
	unsyncIO();
	// cin.exceptions(cin.failbit); 
	// throws exception when do smth illegal
	// ex. try to read letter into int
	if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}

/**
 * Description: euclid finds ${x,y}$ such that $ax+by=\gcd(a,b)$ 
 	* and $|ax|,|by|\le \frac{ab}{\gcd(a,b)}.$ Should work for $a,b<2^{62}$
 * Source: KACTL
 * Time: O(\log ab)
 */

pl euclid(ll a, ll b) { 
	if (!b) return {1,0};
	pl p = euclid(b,a%b); return {p.s,p.f-a/b*p.s}; }
ll invGen(ll a, ll b) { 
	pl p = euclid(a,b); assert(p.f*a+p.s*b == 1); // gcd is 1
	return p.f+(p.f<0)*b; }

/**
 * Description: finds smallest $x\ge 0$ such that $L\le Ax\pmod{P}\le R$
 * Source: https://codeforces.com/gym/102411/submission/64315879
 * Verification: https://codeforces.com/gym/102411/problem/G
 */

ll cdiv(ll x, ll y) { return (x+y-1)/y; }
ll bet(ll P, ll A, ll L, ll R) { 
	if (A == 0) return L == 0 ? 0 : -1;
	ll c = cdiv(L,A); if (A*c <= R) return c;
	ll B = P%A; // P = k*A+B, L <= A(x-Ky)-By <= R 
	// => -R <= By % A <= -L
	auto y = bet(A,B,A-R%A,A-L%A); 
	return y == -1 ? y : cdiv(L+B*y,A)+P/A*y;
}


int solve(ll A, ll X, ll B, ll Y, ll C) {
	ll g = __gcd(A,B);
	A /= g, B /= g; C /= __gcd(g,C);
	F0R(i,2) {
		int t = __gcd(A,C);
		Y /= t; A /= t, C /= t;
		swap(A,B); swap(X,Y);
	}
	assert(__gcd(A,B) == 1 && __gcd(B,C) == 1 && __gcd(C,A) == 1);
	//dbg("OK",A,B,C,X,Y);
	if (C == 1) return X+Y;
	vpi posi; posi.pb({0,C});
	vi step;
	int con = -1LL*A*invGen(B,C)%C; con = (con+C)%C;
	while (posi.bk.s) {
		pi a = posi.bk;
		int L = 1, R = a.s-1; if (L > R) break;
		ll x = bet(C,con,L,R); if (x == -1) break;
		pi b = {x,con*x%C};
		int ti = a.s/(a.s-b.s); if (a.s%(a.s-b.s) == 0) ti --;
		pi c = {a.f+ti*(b.f-a.f),a.s+ti*(b.s-a.s)}; assert(c.s > 0 && c.s <= a.s-b.s);
		posi.pb(c); step.pb(ti);
		//dbg("OOPS",a,b,ti);
		// int rem = con*x%C; 
		// int dem = C-con;
		// int times = rem/dem-(rem%dem == 0);
		// posi.pb({{x,}});
		// dbg("HAHA",posi.bk);
		// 0 < (-A*x)*B^{-1} < posi.bk.s mod C
	}
	assert(posi.bk.s < C);
	step.pb(1);
	posi.pb({C,0});
	//dbg("HA",posi);
	ll ans = 0;
	F0R(i,sz(posi)-1) {
		pi a = posi[i], b = posi[i+1];
		int g = step[i]; // dbg("G",g);
		pi d = {(b.f-a.f)/g,(a.s-b.s)/g}; assert(d.f > 0 && d.s > 0);
		auto ok = [&](ll mid) -> bool {
			if (a.f*mid > X || b.s*mid > Y) return 0;
			ll L = 0, R = g*mid;
			if (b.f*mid > X) ckmin(R,(X-a.f*mid)/d.f);
			if (a.s*mid > Y) ckmax(L,cdiv(a.s*mid-Y,d.s));
			return L <= R;
		};
		ll lo = 0, hi = X+Y;
		while (lo < hi) {
			ll mid = (lo+hi+1)/2;
			if (ok(mid)) lo = mid;
			else hi = mid-1;
		}
		//dbg("AH",a,b,lo,g);
		ckmax(ans,lo);
	}
	return ans;
}


int good(ll A, ll X, ll B, ll Y, ll C) {
	ll g = __gcd(A,B);
	A /= g, B /= g; C /= __gcd(g,C);
	F0R(i,2) {
		int t = __gcd(A,C);
		Y /= t; A /= t, C /= t;
		swap(A,B); swap(X,Y);
	}
	assert(__gcd(A,B) == 1 && __gcd(B,C) == 1 && __gcd(C,A) == 1);
	//dbg("OK",A,B,C,X,Y);
	if (C == 1) return X+Y;
	vpi posi; posi.pb({0,C});
	int con = -1LL*A*invGen(B,C)%C; con = (con+C)%C;
	//dbg("START LOOP");
	while (1) {
		int L = 1, R = posi.bk.s-1; if (L > R) break;
		ll x = bet(C,con,L,R); if (x == -1) break;
		posi.pb({x,con*x%C});
		//dbg("HAHA",posi.bk);
		// 0 < (-A*x)*B^{-1} < posi.bk.s mod C
	}
	//dbg("END LOOP");
	posi.pb({C,0});
	//dbg(posi);
	ll ans = 0;
	trav(t,posi) {
		ll mul = INF;
		if (t.f) ckmin(mul,X/t.f);
		if (t.s) ckmin(mul,Y/t.s);
		ckmax(ans,mul);
	}
	dbg("HAHA",posi);
	F0R(i,sz(posi)-1) {
		pi a = posi[i], b = posi[i+1];
		auto ok = [&](ll mid) -> bool {
			if (a.f*mid > X || b.s*mid > Y) return 0;
			ll L = 0, R = mid;
			if (b.f*mid > X) {
				// a.f*x+b.f*(mid-x) <= X
				// (a.f-b.f)*x+b.f*mid <= X
				// x*(b.f-a.f) >= b.f*mid-X
				L = cdiv(b.f*mid-X,b.f-a.f);
			}
			if (a.s*mid > Y) {
				// a.s*x+b.s*(mid-x) <= Y
				// (a.s-b.s)*x <= Y-b.s*mid
				R = (Y-b.s*mid)/(a.s-b.s);
			}
			return L <= R;
		};
		ll lo = 0, hi = X+Y;
		while (lo < hi) {
			ll mid = (lo+hi+1)/2;
			if (ok(mid)) lo = mid;
			else hi = mid-1;
		}
		dbg(a,b,lo);
		ckmax(ans,lo);
	}
	// dbg("HA",posi);
	return ans;
	// Ax+By is divisible by C
	// what if gcd(A,C) > 1?
	// gcd(B,C) > 1?
}

int main() {
	setIO();
	int T; re(T);
	F0R(i,T) {
		ll A,X,B,Y,C; re(A,X,B,Y,C);
		ll x = solve(A,X,B,Y,C);
		ps(x);
		//dbg(x);
		/*ll y = good(A,X,B,Y,C);
		if (x != y) {
			dbg("OOPS",A,X,B,Y,C);
			dbg(x,y);
			exit(0);
		}*/
	}
	// you should actually read the stuff at the bottom
}

/* stuff you should look for
	* int overflow, array bounds
	* special cases (n=1?)
	* do smth instead of nothing and stay organized
	* WRITE STUFF DOWN
*/



Measured memory_bytes: 3728