Christmas Contest - Team Round - Problem 26

Let ABC be a triangle with area 2023. Points D,E,F are constructed on \overline{AB}, \overline{BC}, \overline{CA}, respectively, such that:

\dfrac{AD}{DB} = \dfrac{BE}{EC} = \dfrac{CF}{FA} = k

for some k<1. Given that [DEF]=637 (the area of \triangle DEF) and k can be written as \frac{a}{b} for relatively prime positive integers a and b, compute the value of 100a+b.