All Tracks Math Combinatorics Inclusion-Exclusion Problem

Non-coprime sequences
Tag(s):

Hard

Problem
Editorial
Analytics

You are given two integers $$n$$, and $$m$$.

Find the number of sequences of length $$ n $$ such that:

  • All elements of the sequence are positive divisors of $$m$$

  • For any two adjacent elements of the sequence, say $$ p $$ and $$ q $$, there exists at least one prime which divides both $$ p $$ and $$ q $$

Print this number modulo $$ 10^9 + 7 $$

Input
The first line of the input contains two integers, $$n$$, and $$m$$ respectively.

Output
Print the number of valid sequences modulo $$10^9 + 7$$

Constraints

  • $$ 1 \le n \le 10^5 $$

  • $$ 1 \le m \le 10^{18} $$

SAMPLE INPUT
2 10
SAMPLE OUTPUT
7
Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Visual Basic

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This Problem was Asked in

IIT Delhi

Challenge Name

ICPC de Tryst

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