Bash got tired on his journey to become the greatest Pokemon master. So he decides to take a break and play with functions.

Bash defines a function f₀(n), which denotes the number of ways of factoring n into two factors p and q such that gcd(p,q)=1. In other words, f₀(n) is the number of ordered pairs of positive integers (p,q) such that p·q=n and gcd(p,q)=1.

But Bash felt that it was too easy to calculate this function. So he defined a series of functions, where f_r+1 is defined as:

Where (u,v) is any ordered pair of positive integers, they need not to be co-prime.

Now Bash wants to know the value of f_r(n) for different r and n. Since the value could be huge, he would like to know the value modulo 10⁹+7. Help him!

The first line contains an integer q (1≤q≤10⁶)− the number of values Bash wants to know.

Each of the next q lines contain two integers r and n (0≤r≤10⁶, 1≤n≤10⁶), which denote Bash wants to know the value f_r(n).

Print q integers. For each pair of r and n given, print f_r(n) modulo 10⁹+7 on a separate line.