The pink soldiers drew (n) circles with their center on the (x)-axis of the plane. Also, they have told that the sum of radii is exactly (m) (^{\text{∗}}). Please find the number of integer points inside or on the border of at least one circle. Formally, the problem is defined as follows. You are given an integer sequence (x_1,x_2,\ldots,x_n) and a positive integer sequence (r_1,r_2,\ldots,r_n), where it is known that (\sum_{i=1}^n r_i = m). You must count the number of integer pairs ((x,y)) that satisfy the following condition. There exists an index (i) such that ((x-x_i)^2 + y^2 \le r_i^2) ((1 \le i \le n)). (^{\text{∗}})Is this information really useful? Don't ask me; I don't really know. Each 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 two integers (n) and (m) ((1 \le n \le m \le 2\cdot 10^5)). The second line of each test case contains (x_1,x_2,\ldots,x_n) — the centers of the circles ((-10^9 \le x_i \le 10^9)). The third line of each test case contains (r_1,r_2,\ldots,r_n) — the radii of the circles ((1 \le r_i), (\sum_{i=1}^n r_i = m)). It is guaranteed that the sum of (m) over all test cases does not exceed (2\cdot 10^5). For each test case, output the number of integer points satisfying the condition on a separate line. On the first test case, the circle with (r_1=1) is completely inside the circle with (r_2=2). Therefore, you only have to count the number of integer points inside the latter. There are (13) integer points such that (x^2+y^2 \le 2^2), so the answer is (13). On the second test case, the circle with (r_1=1) is not completely inside the circle with (r_2=2). There are (3) additional points that are inside the first circle but not inside the second circle, so the