B. Line Segmentstime limit per test1.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPIKASONIC - Lost My Mind (feat.nakotanmaru) You are given two points $$$(p_x,p_y)$$$ and $$$(q_x,q_y)$$$ on a Euclidean plane.You start at the starting point $$$(p_x,p_y)$$$ and will perform $$$n$$$ operations. In the $$$i$$$-th operation, you must choose any point such that the Euclidean distance$$$^{\text{∗}}$$$ between your current position and the point is exactly $$$a_i$$$, and then move to that point.Determine whether it is possible to reach the terminal point $$$(q_x,q_y)$$$ after performing all operations.$$$^{\text{∗}}$$$The Euclidean distance between $$$(x_1, y_1)$$$ and $$$(x_2, y_2)$$$ is $$$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$$InputEach test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows. The first line of each test case contains a single integer $$$n$$$ ($$$1\leq n \leq 10^3$$$) — the length of the sequence $$$a$$$.The second line of each test case contains four integers $$$p_x,p_y,q_x,q_y$$$ ($$$1\leq p_x,p_y,q_x,q_y\leq 10^7$$$) — the coordinates of the starting point and terminal point.The third line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \le a_i \le 10^4$$$) — the distance to move in each operation.It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.OutputFor each test case, output "Yes" if it is possible to reach the terminal point $$$(q_x,q_y)$$$ after all operations; otherwise, output "No".You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.ExampleInput521 1 5 13 331 1 3 32 3 42100 100 100 1004 515 1 1 45210000000 10000000 10000000 1000000010000 10000OutputYes
Yes
No
Yes
Yes
NoteHere is a picture that shows a possible movement of the first test case. The coordinates of point $$$r_1$$$ are $$$(3,1+\sqrt{5})$$$. The first test case. Here is a picture that shows a possible movement of the second test case. The coordinates of point $$$r_1$$$ are $$$(1+\sqrt{3},0)$$$, and the coordinates of point $$$r_2$$$ are $$$\left(-\frac{(\sqrt{3}+4)(3\sqrt{3(149-24\sqrt{3})}-7\sqrt{3}-38)}{104},-\frac{\sqrt{3(1331-764\sqrt{3})}+12\sqrt{3}-27}{104}\right)$$$. The second test case. For the third test case, it can be shown that there is no set of moves that satisfies all requirements.Here is a picture that shows a possible movement of the fourth test case. The fourth test case.