The Dragon King's palace is unlike any structure in the mortal realm. Rather than walls and corridors, its grounds consist of two great circular gardens, each centered around an enchanted fountain. The gardens may overlap, lie apart, or one may even contain the other — the Dragon King enjoys architectural ambiguity.
Once a century, the Dragon King holds his Grand Procession: an honor guard must march in a perfectly straight line, never stepping outside the palace grounds (the union of the two gardens). To impress visiting dignitaries, the procession route must span at least $$$K$$$ units in length.
You are given two circles $$$C_1$$$ and $$$C_2$$$ in the plane, with centers $$$(x_1, y_1)$$$, $$$(x_2, y_2)$$$ and radii $$$r_1$$$, $$$r_2$$$ respectively. Determine whether there exists a line segment of Euclidean length at least $$$K$$$ such that every point on the segment belongs to $$$C_1 \cup C_2$$$ — that is, lies within or on the boundary of at least one of the two gardens.
The first line contains a single integer $$$T$$$ $$$(1 \le T \le 10^3)$$$, the number of procession scenarios the Dragon King wishes to evaluate.
Each test case consists of three lines.
The first line contains three integers $$$x_1$$$, $$$y_1$$$, and $$$r_1$$$ $$$(-10^9 \le x_1,\, y_1 \le 10^9,\ 1 \le r_1 \le 10^6)$$$, the center and radius of the first garden $$$C_1$$$.
The second line contains three integers $$$x_2$$$, $$$y_2$$$, and $$$r_2$$$ $$$(-10^9 \le x_2,\, y_2 \le 10^9,\ 1 \le r_2 \le 10^6)$$$, the center and radius of the second garden $$$C_2$$$.
The third line contains a single integer $$$K$$$ $$$(1 \le K \le 4 \times 10^6)$$$, the minimum required length of the procession route. All values are integers.
For each test case, print YES if a valid procession route exists, NO otherwise.
10 0 50 0 310
YES
10 0 310 0 37
NO
10 0 54 0 512
YES
