401902: GYM100570 A LCM Query

De Prezer loves lcm (Least Common Multiple).Ha has got a sequence a₁, a₂, ..., a_n but doesn't know how to calculate lcm of two numbers.

De Prezer also loves query.So he asks you to answer to m queries on this sequence.

In each query, he gives you number x and you should print the following number :

lcm(a_i, a_i + 1, ..., a_{i + x - 1})

Answer can be very large, so print it modulo 10⁹ + 7 .

The first line of input consists of 2 integers n and m.

The second line of input contains n space separated integers a₁, a₂, ..., a_n.

The next m lines, each line contains an integer x.

1 ≤ n ≤ 2 * 10⁴

1 ≤ m ≤ 10⁶

1 ≤ a_i ≤ 60 (For each 1 ≤ i ≤ n)

1 ≤ x ≤ n

Print m lines, each answer to one query.

5 5
1 2 3 4 5
1
2
3
4
5

1
2
6
12
60

5 5
2 3 1 4 5
1
2
3
4
5

1
3
6
12
60