- Time limit: 1.00 s
- Memory limit: 512 MB
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
Since the input number may be large, it is given as a prime factorization.
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.
Print three integers modulo 10^9+7: the number, sum and product of the divisors.
- 1 \le n \le 10^5
- 2 \le x \le 10^6
- each x is a distinct prime
- 1 \le k \le 10^9
2 2 2 3 1
6 28 1728