import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(int M_) { import std.conv : to; alias M = M_; int x; this(ModInt a) { x = a.x; } this(long a) { x = cast(int)(a % M); if (x < 0) x += M; } ref ModInt opAssign(long a) { return (this = ModInt(a)); } ref ModInt opOpAssign(string op)(ModInt a) { static if (op == "+") { x += a.x; if (x >= M) x -= M; } else static if (op == "-") { x -= a.x; if (x < 0) x += M; } else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } ref ModInt opOpAssign(string op)(long a) { static if (op == "^^") { if (a < 0) return (this = inv()^^(-a)); ModInt t2 = this, te = ModInt(1); for (long e = a; e > 0; e >>= 1) { if (e & 1) te *= t2; t2 *= t2; } x = cast(int)(te.x); return this; } else return mixin("this " ~ op ~ "= ModInt(a)"); } ModInt inv() const { int a = x, b = M, y = 1, z = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } ModInt opUnary(string op: "-")() const { return ModInt(-x); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op)(long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0); } string toString() const { return x.to!string; } } enum MO = 10^^9 + 7; alias Mint = ModInt!MO; // floor(a / b) Int divFloor(Int)(Int a, Int b) { return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0); } // ceil(a / b) Int divCeil(Int)(Int a, Int b) { return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0); } Tuple!(long, long, long) gojo(long a, long b) { if (b == 0) return (a < 0) ? tuple(-a, -1L, 0L) : tuple(a, 1L, 0L); long c = a, d = b, x = 1, y = 0, t; for (; ; ) { t = c / d; c -= t * d; x -= t * y; if (c == 0) { if (d < 0) { d = -d; y = -y; } return tuple(d, y, (d - a * y) / b); } t = d / c; d -= t * c; y -= t * x; if (d == 0) { if (c < 0) { c = -c; x = -x; } return tuple(c, x, (c - a * x) / b); } } } void main() { try { for (; ; ) { const numCases = readInt(); foreach (caseId; 0 .. numCases) { auto A = new long[3]; foreach (i; 0 .. 3) { A[i] = readLong(); } const B = readLong(); A.sort; const res = gojo(A[0], A[1]); const g = res[0]; const w0 = res[1], w1 = res[2]; const p = A[0] / g, q = A[1] / g; assert(A[0] * w0 + A[1] * w1 == g); assert(A[0] * q - A[1] * p == 0); Mint ans; foreach (x2; 0 .. B / A[2] + 1) { const b = B - A[2] * x2; if (b % g == 0) { long x0 = w0 * (b / g); long x1 = w1 * (b / g); assert(A[0] * x0 + A[1] * x1 == b); if (x0 < 0) { const tmp = divCeil(0 - x0, q); x0 += q * tmp; x1 -= p * tmp; } assert(A[0] * x0 + A[1] * x1 == b); if (x1 >= 0) { ans += divFloor(x1 - 0, p) + 1; } } } writeln(ans); } } } catch (EOFException e) { } }