A. Row GCDtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given two positive integer sequences a_1, \ldots, a_n and b_1, \ldots, b_m. For each j = 1, \ldots, m find the greatest common divisor of a_1 + b_j, \ldots, a_n + b_j.InputThe first line contains two integers n and m (1 \leq n, m \leq 2 \cdot 10^5).The second line contains n integers a_1, \ldots, a_n (1 \leq a_i \leq 10^{18}).The third line contains m integers b_1, \ldots, b_m (1 \leq b_j \leq 10^{18}).OutputPrint m integers. The j-th of them should be equal to GCD(a_1 + b_j, \ldots, a_n + b_j).ExampleInput
4 4
1 25 121 169
1 2 7 23
Output
2 3 8 24

4 4
1 25 121 169
1 2 7 23

2 3 8 24 
['math', 'number theory', '*1600']