Number Game

Lots of Numbers. Photo by Black ice

Sitting outside of MS 4000A, you and your friend both arrived $20$ minutes early to your Math 32B class, and have decided to play some math number games. Your friend proposes the following problem:

Given two numbers $N$ and $M$ such that $M \geq N$, find the minimum number of operations it takes to apply on $N$ to yield $M$. Here, one operation is multiplying a number by $2$, adding $1$ to the number or subtracting $1$ from the number.

Being the computer science major you are, you decide to code up a solution to this problem.

The only line of input contains two integers $N$ and $M$ such that $1 \le N \le 10\, 000$ and $1 \le M \le 20\, 000$.

Print a single integer that represents the minimum number of operations it takes to get from $N$ to $M$.

Consider the input $N$ = $2$ and $M$ = $43$, you would have to do $((((((N \times 2) + 1) \times 2) + 1) \times 2) \times 2) - 1$ which is a total of $7$ operations to get to $M$, i.e. $43$.

Sample Input 1 | Sample Output 1 |
---|---|

2 43 |
7 |

Sample Input 2 | Sample Output 2 |
---|---|

12 300 |
9 |