#include using namespace std; #define int long long #define ii pair #define app push_back #define all(a) a.begin(), a.end() #define bp __builtin_popcountll #define ll long long #define mp make_pair #define x first #define y second #define Time (double)clock()/CLOCKS_PER_SEC #define debug(x) std::cout << #x << ": " << x << '\n'; #define FOR(i, n) for (int i = 0; i < n; ++i) #define pb push_back #define trav(a, x) for (auto& a : x) using vi = vector; template std::ostream& operator <<(std::ostream& output, const pair & data) { output << "(" << data.x << "," << data.y << ")"; return output; } template std::ostream& operator <<(std::ostream& output, const std::vector& data) { for (const T& x : data) output << x << " "; return output; } ll div_up(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up ll div_down(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down #define tcT template using V = vector; tcT> void re(V& x) { trav(a, x) cin >> a; } tcT> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } // set a = min(a,b) tcT> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } //need define int long long namespace Stuff { const int MOD = 1e9+7; int mod(int n) { n %= MOD; if (n < 0) return n + MOD; else return n; } int fp(int a, int p) { int ans = 1, c = a; for (int i = 0; (1ll << i) <= p; ++i) { if ((p >> i) & 1) ans = mod(ans * c); c = mod(c * c); } return ans; } int dv(int a, int b) { return mod(a * fp(b, MOD - 2)); } }; struct M { ll x; M (int x_) { x = Stuff::mod(x_); } M () { x = 0; } M operator + (M y) { int ans = x + y.x; if (ans >= Stuff::MOD) ans -= Stuff::MOD; return M(ans); } M operator - (M y) { int ans = x - y.x; if (ans < 0) ans += Stuff::MOD; return M(ans); } M operator * (M y) { return M(x * y.x % Stuff::MOD); } M operator / (M y) { return M(x * Stuff::fp(y.x, Stuff::MOD - 2) % Stuff::MOD); } M operator + (int y) { return (*this) + M(y); } M operator - (int y) { return (*this) - M(y); } M operator * (int y) { return (*this) * M(y); } M operator / (int y) { return (*this) / M(y); } M operator ^ (int p) { return M(Stuff::fp(x, p)); } void operator += (M y) { *this = *this + y; } void operator -= (M y) { *this = *this - y; } void operator *= (M y) { *this = *this * y; } void operator /= (M y) { *this = *this / y; } void operator += (int y) { *this = *this + y; } void operator -= (int y) { *this = *this - y; } void operator *= (int y) { *this = *this * y; } void operator /= (int y) { *this = *this / y; } void operator ^= (int p) { *this = *this ^ p; } bool operator == (M y) { return x == y.x; } }; std::ostream& operator << (std::ostream& o, const M& a) { cout << a.x; return o; } int gcd (int a, int b, int & x, int & y) { if (a == 0) { x = 0; y = 1; return b; } int x1, y1; int d = gcd (b%a, a, x1, y1); x = y1 - (b / a) * x1; y = x1; return d; } signed main() { #ifdef HOME freopen("input.txt", "r", stdin); #else #define endl '\n' ios_base::sync_with_stdio(0); cin.tie(0); #endif int t; cin >> t; while (t--) { vi a(3); re(a); int sum; cin >> sum; sort(all(a)); auto lcm = [&] (int a, int b) { return a * b / __gcd(a, b); }; int A = a[0], B = a[1]; int d = __gcd(A, B); A /= d; B /= d; int x, y; gcd(A, B, x, y); int sx = lcm(A, B) / A; int sy = lcm(A, B) / B; auto get = [&] (int sum) { if (sum % d) return 0ll; int tx = x * (sum/d); int ty = y * (sum/d); // x + k * sx >= 0, k >= -x/sx // y - k * sy >= 0, k <= y/sy int l = div_up(-tx, sx); int r = div_down(ty, sy); if (l <= r) return r - l + 1; else return 0ll; }; M ans = 0; for (int i = 0; i * a.back() <= sum; ++i) { ans += get(sum - i * a.back()); } cout << ans << endl; } }