Numbers

Interview

Time limit1sMemory limit1024 MB

Summary

Given x and a flag k, find the smallest y at least x whose digits are all equal, or all equal except one digit when k is 1.

Level: Medium4 of 10
Topics: Implementation, Brute force, Math
Solved: No attempts yet

Problem

Darina likes numbers whose digits are all the same. For example, she likes $777$ or $5555$ , but she does not like $1234$ at all. When she is in a good mood, she also likes numbers in which all digits except one are the same, such as $77727$ .

Darina has a number $x$ . She wants to find the smallest integer $y \ge x$ that she likes, meaning either all of its digits are the same, or only one of its digits is different from the others.

Write a program numbers that, given an integer $x$ and whether Darina is in a good mood, finds the smallest integer $y \ge x$ that Darina likes.

Input

The first line of standard input contains one integer $x$ . The second line contains one integer $k$ , which is $0$ or $1$ . The value $k = 1$ means Darina is in a good mood, and $k = 0$ means she is not.

Output

The first line of standard output contains one integer $y$ that satisfies the following conditions:

$y \ge x$ .
If $k = 0$ , all digits of $y$ are the same.
If $k = 1$ , all digits of $y$ are the same, except possibly one digit.

Constraints

$100 \le x \le 10^{17}$ .

Examples2

Example 1
Input
```
700
0
```
Expected output
```
777
```
Example 2
Input
```
700
1
```
Expected output
```
700
```