Description

Input

The first line contains $2$ integers $n$ and $q$ ($1 \le n,q \le 10^5$) — the length of the array $a$ and the number of queries.

The next line contains $n$ integers $a_1$, $a_2$, $\ldots$, $a_n$ ($1 \le a_i \le 10^5$) — the elements of the array $a$.

Each of the next $q$ lines contains $2$ integers $l$ and $r$ ($1 \le l \le r \le n$) — the endpoints of this query's interval.

Output

For each query, print its answer on a new line.

6 3
2 3 10 7 5 14
1 6
2 4
3 5

3
1
2

Note

The first query asks about the whole array. You can partition it into $[2]$, $[3,10,7]$, and $[5,14]$. The first subrange has product and LCM equal to $2$. The second has product and LCM equal to $210$. And the third has product and LCM equal to $70$. Another possible partitioning is $[2,3]$, $[10,7]$, and $[5,14]$.

The second query asks about the range $(2,4)$. Its product is equal to its LCM, so you don't need to partition it further.

The last query asks about the range $(3,5)$. You can partition it into $[10,7]$ and $[5]$.