B'Ntarsis has a box B with side lengths x , y , and z . It lies in the 3D coordinate plane, extending from (0,0,0) to (x,y,z) . Ntarsis has a secret box S . He wants to choose its dimensions such that all side lengths are positive integers, and the volume of S is k . He can place S somewhere within B such that: S is magical, so when placed at an integer location inside B , it will not fall to the ground. Among all possible ways to choose the dimensions of S , determine the maximum number of distinct locations he can choose to place his secret box S inside B . Ntarsis does not rotate S once its side lengths are selected. The first line consists of an integer t , the number of test cases ( 1 <= q t <= q 2000 ). The description of the test cases follows. The first and only line of each test case contains four integers x, y, z and k ( 1 <= q x, y, z <= q 2000 , 1 <= q k <= q x cdot y cdot z ). It is guaranteed the sum of all x , sum of all y , and sum of all z do not exceed 2000 over all test cases. Note that k may not fit in a standard 32-bit integer data type. For each test case, output the answer as an integer on a new line. If there is no way to select the dimensions of S so it fits in B , output 0 . For the first test case, it is optimal to choose S with side lengths 2 , 2 , and 2 , which has a volume of 2 cdot 2 cdot 2 = 8 . It can be shown there are 8 ways to put S inside B . The coordinate with the least x , y , and z values for each possible arrangement of S are: The arrangement of S with a coordinate of (0, 0, 0) is depicted below: For the second test case, S with side lengths 2 , 3 , and 3 are optimal. '...