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  1. Prepare
  2. Functional Programming
  3. Recursion
  4. Super Digit

Super Digit

We define super digit of an integer using the following rules:

  • If has only digit, then its super digit is .
  • Otherwise, the super digit of is equal to the super digit of the digit-sum of . Here, digit-sum of a number is defined as the sum of its digits.

For example, super digit of will be calculated as:

super_digit(9875) = super_digit(9+8+7+5) 
                  = super_digit(29) 
                  = super_digit(2+9)
                  = super_digit(11)
                  = super_digit(1+1)
                  = super_digit(2)
                  = 2.

You are given two numbers and . You have to calculate the super digit of .

is created when number is concatenated times. That is, if and , then .

Input Format

The first line contains two space separated integers, and .

Constraints

Output Format

Output the super digit of , where is created as described above.

Sample Input 0

148 3

Sample Output 0

3

Explanation 0

Here and , so . 

super_digit(P) = super_digit(148148148) 
               = super_digit(1+4+8+1+4+8+1+4+8)
               = super_digit(39)
               = super_digit(3+9)
               = super_digit(12)
               = super_digit(1+2)
               = super_digit(3)
               = 3.