7657: [CSES Problem Set] Divisor Analysis
[Creator : ]
Description
Given an integer, your task is to find the number, sum and product of its divisors. As an example, let us consider the number $12$:
-
the number of divisors is $6$ (they are $1, 2, 3, 4, 6, 12$)
-
the sum of divisors is $1+2+3+4+6+12=28$
-
the product of divisors is $1 \cdot 2 \cdot 3 \cdot 4 \cdot 6 \cdot 12 = 1728$
Input
The first line has an integer $n$: the number of parts in the prime factorization.
After this, there are $n$ lines that describe the factorization. Each line has two numbers $x$ and $k$ where $x$ is a prime and $k$ is its power.
After this, there are $n$ lines that describe the factorization. Each line has two numbers $x$ and $k$ where $x$ is a prime and $k$ is its power.
Output
Print three integers modulo $10^9+7$: the number, sum and product of the divisors.
Constraints
$1≤n≤10^5$
$2 \le x \le 10^6$
each $x$ is a distinct prime
$1 \le k \le 10^9$
$2 \le x \le 10^6$
each $x$ is a distinct prime
$1 \le k \le 10^9$
Sample 1 Input
2
2 2
3 1
Sample 1 Output
6 28 1728