Dramatic Multiplication

Time limit2sMemory limit128 MB

Summary

Find the smallest positive integer X ending in digit k such that multiplying X by n equals X with its last digit moved to the front.

Level: Medium5 of 10
Topics: Math, Number theory, Simulation
Solved: No attempts yet

Problem

For a positive integer X, let R(X) be the number obtained by moving the last decimal digit of X to the front. For example, if X = 102564, then R(X) = 410256.

A positive integer X is called n-dramatic if n × X = R(X).

Given n and k, find the smallest n-dramatic number whose last digit is k. If no such number exists, print 0. The decimal representation of the number cannot start with 0.

Input

The first line contains n and k separated by a space.

1 ≤ n ≤ 9, 1 ≤ k ≤ 9

Output

Print the smallest n-dramatic number whose last digit is k. If no such number exists, print 0.

Examples2

Example 1
Input
```
4 5
```
Expected output
```
128205
```
Example 2
Input
```
2 1
```
Expected output
```
0
```