Required Length

Description:

Input:

The only line of the input contains two integers $$$n$$$ and $$$x$$$ ($$$2 \le n \le 19$$$; $$$1 \le x < 10^{n-1}$$$).

Output:

Print one integer — the minimum number of operations required to make the length of decimal representation of $$$x$$$ (without leading zeroes) equal to $$$n$$$, or $$$-1$$$ if it is impossible.

Sample Input:

2 1

Sample Output:

-1

Sample Input:

3 2

Sample Output:

4

Sample Input:

13 42

Sample Output:

12

Note:

In the second example, the following sequence of operations achieves the goal:

1. multiply $$$x$$$ by $$$2$$$, so $$$x = 2 \cdot 2 = 4$$$;
2. multiply $$$x$$$ by $$$4$$$, so $$$x = 4 \cdot 4 = 16$$$;
3. multiply $$$x$$$ by $$$6$$$, so $$$x = 16 \cdot 6 = 96$$$;
4. multiply $$$x$$$ by $$$9$$$, so $$$x = 96 \cdot 9 = 864$$$.