## Goal

Your goal is to build an arithmetic expression which evaluates to `N`. This expression can only contain copies of `a`, the four arithmetic operations (+, -, * and /) and parentheses ( ).

What is the minimum number of copies of `a` needed to reach the target number `N`?

**Note:** Divisions are valid only if the result is an integer. Thus, 8 / 4 is valid and 10 / 3 is not.

Examples:

N = 69, a = 3

( 3 * 3 + 3 ) * ( 3 + 3 ) - 3 = 69

Answer is **6**

N = 41, a = 6

6 * 6 + 6 - 6 / 6 = 41

Answer is **5**

N = 888, a = 8

( 8 + 8 ) * ( 8 * 8 - 8 ) - 8 = 888

Answer is **6**

N = 1000, a = 11

( 11 * 11 - 11 - 11 + 11 / 11 ) * ( 11 - 11 / 11 ) = 1000

Answer is **9**

N = 666, a = 7

7 * 7 * ( 7 + 7 ) - 7 - 7 - 7 + 7 / 7 = 666

Answer is **9**

This problem could get tough. example:

N = 3662, a = 71 needs 17 '71'...

But none of the test cases proposed here are that bad!
Input

**Line 1:** the target integer `N`

**Line 2:** the integer `a` to use in your computation

Output

**Line 1:** the minimum number of `a` used to obtain `N`

Constraints

1 < `N` <= 10000

1 <= `a` <= 100

solution <= 12