The Intersection

A given coefficient K leads an intersection of two curves f(x) and gK(x). In the first quadrant, the curve f is a monotone increasing function that f(x)=√x. The curve g is decreasing and g(x)=K/x.
To calculate the x-coordinate of the only intersection in the first quadrant is the following question. For accuracy, we need the nearest rational number to x and its denominator should not be larger than 100000.

The first line is an integer T (1≤T≤100000) which is the number of test cases.
For each test case, there is a line containing the integer K (1≤K≤100000), which is the only coefficient.

For each test case, output the nearest rational number to x. Express the answer in the simplest fraction.

5
1
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5

1/1
153008/96389
50623/24337
96389/38252
226164/77347