Problem Statement

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 $a_0=N$, $a_{i+1}=f(a_i)\ (i\geq 0)$.

Constraints

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

Input

Input is given from Standard Input in the following format:

N K

Output

Print $a_K$.