Machine

A machine has a screen initially displaying the number $1$. The machine has two buttons: the left button adds $3$ to the number and the right button multiplies the number by $2$.

Your task is to reach a given number $x$ by pushing the buttons. What is the smallest number of pushes needed?

For example, when $x=17$, an optimal solution is the following:

• The initial number is $1$.
• Push the left button to get the number $4$.
• Push the left button to get the number $7$.
• Push the right button to get the number $14$.
• Push the left button to get the number $17$.

In this case, the smallest number of pushes is $4$.

In a file machine.py, implement the function min_steps that finds the smallest number of pushes to reach the number $x$. If no sequence of pushes can achieve $x$, the function should return $-1$.

The function should be efficient when $x$ is in the range $1 \dots 1000$.

def min_steps(x):
    # TODO

if __name__ == "__main__":
    print(min_steps(1)) # 0
    print(min_steps(2)) # 1
    print(min_steps(3)) # -1
    print(min_steps(4)) # 1
    print(min_steps(5)) # 2
    print(min_steps(17)) # 4
    print(min_steps(42)) # -1
    print(min_steps(100)) # 7
    print(min_steps(1000)) # 13