Consider the Function:
$$ F(X) $$ = Number of Divisors of Integer $$'X'$$
You have been given an array consisting of $$N$$ integers and $$M$$ queries .There can be only 1 type of query i.e :
$$query(l,r)$$ : You need to find product of all number in the range from $$l$$ to $$r$$ inclusive and then output the result of function $$F(X)$$ mod $$10^9 +7 $$ for that product.
The first line contains 2 integers $$N$$ and $$M$$ denoting the number of array elements and the number of queries The next line contains $$N$$ numbers denoting the elements of the array .
Each of the next M lines contains 2 integers $$l$$ and $$r$$ for whom the query needs to be answered.
For each query you need to print a single number denoting the answer to that query mod $$10^9 +7$$
$$ 1\le N \le 5*10^5 $$
$$1 \le M \le 4*10^5 $$
$$ 1 \le l \le r \le N $$
$$ 1 \le a[i] \le 10 $$
Note: Each element of the array shall not have a value greater than 10.
For the 1st query, the product is 2 , F(2)=2. For the second query , product=720 , F(720)=30.