Super Digit

You are given a number n as a string and an integer k. Construct a new number P by concatenating n with itself k times. In mathematical notation, this can be written as:

$$P = \underbrace{n \| n \| \cdots \| n}_{k \text{ times}} $$

The super digit of a number is defined recursively as follows:

$$\text{superdigit}(x)=\begin{cases} x, & \text{if } x < 10 \\ \text{superdigit}\Big(\sum_{i} (\text{digit}_i)\Big), & \text{otherwise} \end{cases} $$

Your task is to compute the super digit of the number P formed by concatenating n k times.

inputFormat

The input is read from stdin and consists of a single line containing a string n and an integer k separated by a space.

Example:

148 3

outputFormat

Output to stdout the super digit of the constructed number P as a single integer.

Example:

3

## sample

123 1

6

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