We define super digit of an integer $\boldsymbol{x}$ using the following rules:

Given an integer, we need to find the super digit of the integer.

If $\boldsymbol{x}$ has only $\mbox{I}$ digit, then its super digit is $\boldsymbol{x}$.
Otherwise, the super digit of $\boldsymbol{x}$ is equal to the super digit of the sum of the digits of $\boldsymbol{x}$.

For example, the super digit of $9875$ will be calculated as:

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

Example

$n='\:9875'$

$k=4$

The number $\boldsymbol{p}$ is created by concatenating the string $n$ $\boldsymbol{\mbox{k}}$ times so the initial $p=9875987598759875$.

superDigit(p) = superDigit(9875987598759875)
              9+8+7+5+9+8+7+5+9+8+7+5+9+8+7+5 = 116
superDigit(p) = superDigit(116)
              1+1+6 = 8
superDigit(p) = superDigit(8)

All of the digits of $\boldsymbol{p}$ sum to $\textbf{116}$. The digits of $\textbf{116}$ sum to $8$. $8$ is only one digit, so it is the super digit.

Function Description

Complete the function superDigit in the editor below. It must return the calculated super digit as an integer.

superDigit has the following parameter(s):

string n: a string representation of an integer
int k: the times to concatenate $n$ to make $\boldsymbol{p}$

Returns

int: the super digit of $n$ repeated $\boldsymbol{\mbox{k}}$ times

Input Format

The first line contains two space separated integers, $n$ and $\boldsymbol{\mbox{k}}$.

Constraints

$1\leq n<10^{100000}$
$1\leq k\leq10^5$

Sample Input 0
148 3

Sample Output 0
3

Explanation 0

Here $n=148$ and $k=3$, so $p=148148148$.

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

Sample Input 1
9875 4

Sample Output 1
8

Sample Input 2
123 3

Sample Output 2
9

Explanation 2

Here $n=123$ and $k=3$, so $p=123123123$.

super_digit(P) = super_digit(123123123)
= super_digit(1+2+3+1+2+3+1+2+3)
= super_digit(18)
= super_digit(1+8)
= super_digit(9)
= 9

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