Fractions#1269

Fractions

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A fraction $\frac{a}{b}$ \frac{a}{b} ( $0 < a < b \leq 100$ 0 < a < b \leq 100) can be represented as a sum of unit fractions:

\frac{1}{b _{1}} + \frac{1}{b _{2}} + \dots + \frac{1}{b _{n}} .

\frac{1}{b_1} + \frac{1}{b_2} + \ldots + \frac{1}{b_n}.

Find such a representation where the sum $b_{1} + b_{2} + \dots + b_{n}$ b_1 + b_2 + \ldots + b_n is minimized.

Input

Each test case contains two positive integers $a$ and $b$ ( $0 < a < b \leq 100$ 0 < a < b \leq 100).

For each test case, output the minimal sum.

Example 1

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\frac{a}{b}

0 < a < b \leq 100

\frac{1}{b _{1}} + \frac{1}{b _{2}} + \dots + \frac{1}{b _{n}} .

b_{1} + b_{2} + \dots + b_{n}

0 < a < b \leq 100