The annual Christmas light show is happening this weekend! The light show consists of a line of ~N~ lights arranged in a row numbered from ~1~ to ~N~.

To ensure a colourful celebration, the lights have been programmed to turn on with a certain pattern. A light with value ~a_i~ will only be on at a second which is a multiple of ~a_i~. Time starts at second ~0~.

To test out the function of the lights there are ~Q~ scenarios. The ~i~-th scenario asks for the index of the first light from the left that will be off during second ~t_i~. If all lights will be on, output -1.

Constraints

~1 \le N \le 2 \cdot 10^5~

~1 \le Q \le 10^6~

~1 \le a_i \le 10^9~

~0 \le t_i \le 10^9~

Input Specification

The first line contains two space-separated integers, ~N~ and ~Q~.

The second line contains ~N~ space-separated integers ~a_i~.

The next ~Q~ lines contain ~t_i~.

Output Specification

For each scenario, if all the lights are on, output -1.

Otherwise, output the index of the first light off from the left.

Sample Input 1

4 2
2 4 6 8
4
24

Sample Output 1

3
-1

Explanation for Sample 1

For the first scenario, we can see that ~4~ is a multiple of ~2~ and ~4~ but not ~6~. Therefore the ~3~-rd light is the first light from the left that is off.

For the second scenario, we can see that ~24~ is a multiple of ~2~, ~4~, ~6~, and ~8~. Therefore, all lights are on and we can output -1.

Sample Input 2

5 1
72 7 69 4 20
0

Sample Output 2

-1