Negative number bases are just like positive ones, except that every other place value is negative.

The number seven represented in positive base two is $111_2$. In base negative two, however, the place values mean that $7$ is represented as $11011_{-2}$. This is because $1\cdot16+1\cdot(-8)+0\cdot4+1\cdot(-2)+1=7$.

Negative number bases can represent both positive and negative integers without using a sign. Negative-base representations do not use a sign in this task. Write a program to convert an ordinary integer into the supplied base.

Input

A single line with two integers $N$ and $B$: $-30000\le N\le30000$ is the number to convert, expressed in base $10$; the new base satisfies $-10\le B\le-2$ or $2\le B\le10$.

Output

A single line containing the representation of $N$ in base $B$.

Examples

Input 1

7 -2

Output 1

11011