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)\ $(i\geq 0)$.

Input

Input is given from Standard Input in the following format:
N K

Output

Print a_K.

Constraints

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

Sample Input 1

314 2

Sample Output 1

693

We have:

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

Sample Input 2

1000000000 100

Sample Output 2

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
• $\vdots$

Sample Input 3

6174 100000

Sample Output 3

6174

见题面 Input 部分

见题面 Output 部分