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Time Limit: 2 s Memory Limit: 512 MB Total points: 100 Hackable ✓

#21652. 【PR #4】Is There Really a Nine

The problem was used in the following contests:

Public Round #4

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

For a positive integer $k$, a magic number $x$ is defined as a positive integer such that the decimal representation of $x \times (10^k - 1)$ does not contain the digit $9$. You need to find the $n$-th magic number.

Input

A single line containing two integers $k$ and $n$.

Output

A single line containing the $n$-th magic number.

Examples

Input 1

1 8

Output 1

Input 2

5 84

Output 2

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