Remainder of polynomial division (noch nicht übersetzt)

For positive integers n and m, we define two polynomials F_n(x) = xⁿ and G_m(x) = (x-1)^m.
We also define a polynomial R_n,m(x) as the remainder of the division of F_n(x) by G_m(x).
For example, R_6,3(x) = 15x² - 24x + 10.

Let C(n, m, d) be the absolute value of the coefficient of the d-th degree term of R_n,m(x).
We can verify that C(6, 3, 1) = 24 and C(100, 10, 4) = 227197811615775.

Find C(10¹³, 10¹², 10⁴) mod 999999937.