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Find a fraction with the smallest denominator

Input

Two non-negative floating point numbers \$x < y\$. You can assume they are close enough to each other that there is no integer between \$x\$ and \$y\$.

Output

A fraction with the smallest possible denomination that lies strictly between \$x\$ and \$y\$.

Examples

Input: 1 and 2

Output: 3/2

Input: 0 and 0.33

Output: 1/4

Input: 0.4035 and 0.4036

Output: 23/57

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\$\begingroup\$ Which is fortunate since ⌈xd⌉<yd is the wrong test. \$\endgroup\$

Neil
– Neil

2024年01月12日 23:49:45 +00:00
Commented Jan 12, 2024 at 23:49

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