#C11127. Sum and Product of Digits of Primes

    ID: 40409 Type: Default 1000ms 256MiB

Sum and Product of Digits of Primes

Sum and Product of Digits of Primes

You are given two integers \(n\) and \(m\) representing the boundaries of a range \([n, m]\) (inclusive). Your task is to:

  1. Find all prime numbers in the range \([n, m]\).
  2. Calculate the sum of these prime numbers.
  3. Concatenate all the prime numbers into a single number (in their natural order) and calculate the product of the digits in this concatenated number.

If there are no prime numbers in the range, output the sum as 0 and the product as 1.

Note: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

inputFormat

The input consists of a single line containing two space-separated integers \(n\) and \(m\) (with \(n \le m\)).

outputFormat

Output a single line with two space-separated integers: the sum of all prime numbers in the range and the product of the digits of these prime numbers (when concatenated). If no prime numbers exist in the range, output 0 1.

## sample
10 20
60 189