622. Mayank Bhaiya's Magic Numbers

0

Medium

Mayank Bhaiya is fascinated by numbers that have the same difference between every two consecutive digits. He needs your help to find all such numbers.

Given two integers N and k, you are required to print an array of all integers of length N where the difference between every two consecutive digits is k. The array should be printed in

Given two integers N and k, you are required to print an array of all integers of length N where the difference between every two consecutive digits is k. The array should be printed in

**sorted**order. Please note that the integers should not have leading zeros, so numbers like 02 and 043 are not allowed.Input Format

The first line contains two space-separated integers N and K.

Output Format

Print the desired output array.

Example

Input

3 7

Output

181 292 707 818 929

Constraints

2 <= N <= 9

0<= k <= 9

0<= k <= 9

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