With fast developments of information and communication technology, many cities today have established bicycle sharing systems. The key component of the system is to provide information on nearby bicycles to potential users.
Consider mmm bicycles and nnn customers, where each bicycle is located at coordinate (cj,dj)(c_j , d_j )(cj?,dj?) for j=1,2,...,m,j = 1, 2, ... , m,j=1,2,...,m, and each user iii is located at coordinate (ai,bi)(a_i, b_i)(ai?,bi?) for i=1,2,...,ni = 1, 2, ... , ni=1,2,...,n The distance between two coordinates (x,y)(x, y)(x,y) and (x,y)(x, y)(x,y) is measured by (x?x)2+(y?y)2 \sqrt{(x-x)^2 +(y-y)^2}(x?x)2+(y?y)2 ?. For each user i=1,2,...,ni = 1,2,...,ni=1,2,...,n, you are given a threshold sis_isi?, your task is to return the total number of bicycles that are within a distance of si from user iii.
Input
The test data may contain many test cases. Each test case contains four lines. The first line of each case contains two integers, mmm and n(0<m,n≤1000)n (0 < m, n \le 1000)n(0<m,n≤1000). The second line contains the coordinates, (c1,d1),(c2,d2),...,(cm,dm)(c_1, d_1), (c_2, d_2), ... , (c_m, d_m)(c1?,d1?),(c2?,d2?),...,(cm?,dm?), of bicycles 1,2,...,m 1, 2, ... , m1,2,...,m, respectively, which are separated by a space. The third line contains the coordinates,(a1,b1),(a2,b2),...,(an,bn)(a1, b1), (a2, b2), ... , (an, bn)(a1,b1),(a2,b2),...,(an,bn), of users 1,2,...,n1, 2,... , n1,2,...,n, respectively, which are separated by a space. contains the thresholds, s1,s2,...,sns_1, s_2, ... , s_ns1?,s2?,...,sn?, of the nnn users. The last test case is followed by a line of two 000s. All the number of coordinate in the input is in the range [?100000,100000][-100000, 100000]