G. Running Competitiontime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputA running competition is going to be held soon. The stadium where the competition will be held can be represented by several segments on the coordinate plane:  two horizontal segments: one connecting the points (0, 0) and (x, 0), the other connecting the points (0, y) and (x, y);  n + 1 vertical segments, numbered from 0 to n. The i-th segment connects the points (a_i, 0) and (a_i, y); 0 = a_0 < a_1 < a_2 < \dots < a_{n - 1} < a_n = x. For example, here is a picture of the stadium with x = 10, y = 5, n = 3 and a = [0, 3, 5, 10]:  A lap is a route that goes along the segments, starts and finishes at the same point, and never intersects itself (the only two points of a lap that coincide are its starting point and ending point). The length of a lap is a total distance travelled around it. For example, the red route in the picture representing the stadium is a lap of length 24.The competition will be held in q stages. The i-th stage has length l_i, and the organizers want to choose a lap for each stage such that the length of the lap is a divisor of l_i. The organizers don't want to choose short laps for the stages, so for each stage, they want to find the maximum possible length of a suitable lap.Help the organizers to calculate the maximum possible lengths of the laps for the stages! In other words, for every l_i, find the maximum possible integer L such that l_i \bmod L = 0, and there exists a lap of length exactly L.If it is impossible to choose such a lap then print -1.InputThe first line contains three integers n, x and y (1 \le n, x, y \le 2 \cdot 10^5, n \le x).The second line contains n + 1 integers a_0, a_1, ..., a_n (0 = a_0 < a_1 < a_2 < \dots < a_{n - 1} < a_n = x).The third line contains one integer q (1 \le q \le 2 \cdot 10^5) — the number of stages.The fourth line contains q even integers l_1, l_2, ..., l_q (4 \le l_i \le 10^6) — the lengths of the stages. OutputPrint q numbers. The i-th number should be equal to the maximum possible length of a suitable lap for the i-th stage, or -1 if it is impossible to choose a lap for that stage.ExampleInput
3 10 5
0 3 5 10
6
24 30 14 16 18 10
Output
24 30 14 16 -1 -1 
3 10 5
0 3 5 10
6
24 30 14 16 18 10

24 30 14 16 -1 -1 
['bitmasks', 'fft', 'math', 'number theory', '*2600']