Aftermath

문제

Once upon a time, you had a nice positive integer $n$.

Since you like division, you quickly found all its positive integer divisors.

Not being a mean guy, you calculated $a$ --- the arithmetic mean of divisors of $n$. Surprisingly, this number turned out to be an integer.

Some time passed, and you calculated $h$ --- the harmonic mean of divisors of $n$. Even more surprisingly, this number turned out to be an integer, too!

Unfortunately, your memory let you down, and now you remember $a$ and $h$ but don't remember $n$. However, you remember that $n$ didn't exceed ${10}^{15}$.

Your muse suggested to bring good old times back and restore any value of $n$ matching your records.

입력

The first line of the input contains a single positive integer $a$.

The second line of the input contains a single positive integer $h$.

It's guaranteed that there exists a positive integer $n\le {10}^{15}$ such that the arithmetic mean of divisors of $n$ is equal to $a$, which the harmonic mean of divisors of $n$ is equal to $h$.

출력

Output any positive integer $n$ not exceeding ${10}^{15}$ which doesn't contradict the given information.

힌트

The arithmetic mean is the sum of a collection of numbers divided by the number of numbers in the collection. For example, the arithmetic mean of 1, 2, 3 and 6 is equal to $\frac{1+2+3+6}{4}=3$.

The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of numbers in the collection. For example, the harmonic mean of 1, 2, 3 and 6 is equal to $(\frac{1^{-1}+2^{-1}+3^{-1}+6^{-1}}{4}{)}^{-1}=2$.

Thus, in the first example test case, $n=6$ satisfies the requirements since its divisors are 1, 2, 3 and 6.

예제 입력 1 복사

3
2

예제 출력 1 복사

6