P8629 [Lанqiao Cup 2015 National C] Robot Reproduction

Robots in the X galaxy can copy themselves automatically. In $1$ year, each robot can reproduce $2$ copies of itself, and then it loses the ability to reproduce. Every year, the X galaxy will select $1$ newly born robot and send it into space. That is, if the X galaxy originally has $5$ robots, then: After $1$ year, the total number is: $5 + 9 = 14$. After $2$ years, the total number is: $5 + 9 + 17 = 31$. If you have already observed that after $n$ years the total number of robots is $s$, can you calculate how many robots there were at the beginning?

Input one line with two numbers $n$ and $s$, separated by spaces, with the meanings as described above. $n$ is not greater than $100$, and $s$ has at most $50$ digits.

Output one line with one integer, indicating how many robots there were at the beginning.

Time limit: $1$ second, $512\text{M}$. Lanqiao Cup 2015, 6th National Finals. Translated by ChatGPT 5