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.

Input Format:

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.

Output Format:

For each query you need to print a single number denoting the answer to that query mod \(10^9 +7\)

Constraints:

\( 1\le N \le 5*10^5 \)

\(1 \le M \le 4*10^5 \)

\( 1 \le l \le r \le N \)

\( 1 \le a[i] \le 10 \)

Note: Each element of the array shall not have a value greater than 10.