For an integer $x$ not less than $0$, we define $g_1(x), g_2(x), f(x)$ as follows:

-   $g_1(x)=$ the integer obtained by rearranging the digits in the decimal notation of $x$ in descending order
-   $g_2(x)=$ the integer obtained by rearranging the digits in the decimal notation of $x$ in ascending order
-   $f(x)=g_1(x)-g_2(x)$

For example, we have $g_1(314)=431$, $g_2(3021)=123$, $f(271)=721-127=594$. Note that the leading zeros are ignored.

Given integers $N, K$, find $a_K$ in the sequence defined by $a_0=N$, $a_{i+1}=f(a_i)\ (i\geq 0)$.

Input is given from Standard Input in the following format:

```
$N$ $K$
```

Print $a_K$.

-   $0 \leq N \leq 10^9$
-   $0 \leq K \leq 10^5$
-   All values in input are integers.

693

We have:

• $a_0=314$
• $a_1=f(314)=431−134=297$
• $a_2=f(297)=972−279=693$

0

We have:

• $a_0=1000000000$
• $a_1=f(1000000000)=1000000000−1=999999999$
• $a_2=f(999999999)=999999999−999999999=0$
• $a_3=f(0)=0−0=0$
• ⋮