It has two parts to this problem. You are given $n$ and $k$. You have to tell the minimum number of pieces, $a$, you can cut a sandwich of length $n$ such that the length of no piece is greater than $k$. The answer is quite simple, isn’t it ? Answer of the first part click to hide $a = \lceil \frac{n}{k} \rceil$ The second part is, how many ways we can cut the sandwich into $a$ pieces such that the length of no piece is greater than $k$.

Statement: In this problem you are asked to calculate : $\sum_{i=L}^{R}{\sum_{j=0}^{i}{[\binom{i}{j} \text{ (mod 2)} \equiv 0]}}$ , for given $L$ and $R$. Inside Math: From the lucas' theorem we can state that, $\sum_{j=0}^{i}{[\binom{i}{j} \text{ (mod 2)}\equiv 1]} = 2^{f(i)}$ . [$f(i) = \text{ number of one in binary representation of } i$] Suppose , $S(x) = \sum_{i=0}^{x}{\sum_{j=0}^{i}{[\binom{i}{j} \text{ (mod 2)} \equiv 0]}}$ . Hence , our answer will be $S(R)-S(L-1)$