1612: Bash Plays with Functions
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
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 fr+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 fr(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 fr(n).
Print q integers. For each pair of r and n given, print fr(n) modulo 109+7 on a separate line.
5
0 30
1 25
3 65
2 5
4 48
8
5
25
4
630