The Exam

Professor Byteoni is preparing the Bit & Byte Theory exam. He has already written $n$ questions and gave each one an expected difficulty coefficient. The coefficients are the natural numbers $1$ to $n$, and no two questions share a coefficient.

Now he is deciding in what order the questions go on the paper. He wants his students to judge the difficulty of every question on their own, so he plans to line the questions up so that the coefficients of two consecutive questions differ by at least $k$. He also wants to know how strict such a requirement can get on $n$ questions.

The first and only input line contains two integers $n$ and $k$ ($2 \le n \le 10^6$, $1 \le k \le n$): the number of questions the professor prepared and the smallest difference he wants between the coefficients of two consecutive questions.

Print one line with the largest integer $d$ such that all $n$ questions can be lined up so that the coefficients of every two consecutive questions differ by at least $d$. If that $d$ is smaller than $k$, the professor cannot meet his own requirement, so print the single word NIE (Polish for no) instead.