- Time limit: 1.00 s
- Memory limit: 512 MB
- 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.
Output
Print three integers modulo $10^9+7$: the number, sum and product of the divisors.
Constraints
- $1 \le n \le 10^5$
- $2 \le x \le 10^6$
- each $x$ is a distinct prime
- $1 \le k \le 10^9$
Input:
2
2 2
3 1
Output:
6 28 1728