Problem Description

One of the most basic and simple technical statistics in baseball is the “batting average”. A “hit” means that the batter hits the ball pitched by the pitcher into fair territory, and the batter can reach at least first base safely. Since a team can score only when a player returns to home plate, hits are the most important way to score runs. Therefore, batting average is also a very important statistic for a batter. As the name suggests, batting average is the ratio of the number of hits to the number of at-bats. If a batter gets $1$ hit in $5$ at-bats, then their batting average is $0.2$.

Uruto is an amateur baseball fan. Once, during training, he saw his own batting average statistic. He found that this value was rounded to $n$ digits after the decimal point. Uruto wants to know: at least how many at-bats could have produced such a batting average.

Input Format

The input file contains multiple test cases.

• Each test case occupies one line and contains an integer $n$ and a floating-point number $r$. Here, $r$ is a decimal with $n$ digits after the decimal point, representing an approximate value of Uruto’s batting average.

Output Format

For each test case, output one integer on a separate line, representing the minimum possible number of at-bats for Uruto.

2 0.33
3 0.316

3
19

Hint

For $20\%$ of the testdata, the answer is guaranteed to be within $1000$.

For all testdata, it is guaranteed that $0<n\leq 15$, and the number of test cases is within $500$.

If a baseball player’s batting average is above $30\%$, then they are definitely a key player on the team. With this in mind, it is guaranteed that for all testdata, $0\leq r<1$.

Translated by ChatGPT 5