While studying the topic of "binary representation of numbers," an informatics teacher came up with the following problem. You are given two numbers $N$ and $M$. Find the index of the first occurrence (from the left) of the binary code of $M$ in the binary code of $N$, assuming that both binary codes do not contain leading zeros. Can you handle this task?

Input

A single line containing two non-negative integers $N$ and $M$ separated by a space, where $0 \leqslant M \leqslant N \leqslant 10^{19}$.

Output

A single integer — the index of the first occurrence of the binary code of $M$ in the binary code of $N$. The index of the leftmost position in $N$ is considered to be $0$. If there is no occurrence, output $-1$.

Examples

Input 1

6 2

Output 1

1