## Remainder of polynomial division

### Problem 498

For positive integers `n` and `m`, we define two polynomials F_{n}(`x`) = `x`^{n} 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`) = 15`x`^{2} - 24`x` + 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(10^{13}, 10^{12}, 10^{4}) mod 999999937.