Hello Codeforcers! As a student of department of mathematics, I'd like to demonstrate an application of Extended Field.

First we should include the idea of splitting field, a splitting field F of a polynomial P is the smallest field such that

.

In the other word, P decomposes into linear factor under this field.

For example, P = x² + 1 does not split over but splitting over

Once a splitting field implementation is done, we can FFT under module more than