Author: | A. Baranov | Time limit: | 1 sec | |
Input file: | Standard input | Memory limit: | 256 Mb | |
Output file: | Standard output |
The scientists of Flatland have discovered that the universe they live in is topologically similar to the surface of a torus.
This means that along each coordinate axis x and y, the periodicity condition is satisfied with a respective period Lx and Ly.
In other words, points at coordinates (x+u⋅Lx,y+v⋅Ly) with any integer values u and v are identical.
For the purpose of a scientific experiment, a ray is emitted from a point with coordinates (0,0), directed by the vector →D=(dx,dy).
It is required to determine the distance the ray will travel before reaching the initial point.
The result should be expressed in units equal to the length of the vector →D,
In other words, the task is to find the minimum coefficient λ>0, such that by shifting the vector, one can reach the initial point.
The obtained number should be represented as an irreducible fraction: λ=αβ.
The beginning of the input data contains a natural numbe n, followed by exactly n queries,
each specified by a set of integers: Lxi, Lyi, dxi и dyi.
The output data should contain the values αi и βi,
obtained in response to each i-th query.
1≤(Lxi,Lyi)≤106, −106≤(dxi,dyi)≤106,
|dxi|+|dyi|>0,
1≤n≤105.
No. | Standard input | Standard output |
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1 |
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