Problem 498
Remainder of polynomial division
For positive integers n and m, we define two polynomials Fn(x) = xn and Gm(x) = (x-1)m.
We also define a polynomial Rn,m(x) as the remainder of the division of Fn(x) by Gm(x).
For example, R6,3(x) = 15x2 - 24x + 10.
Let C(n, m, d) be the absolute value of the coefficient of the d-th degree term of Rn,m(x).
We can verify that C(6, 3, 1) = 24 and C(100, 10, 4) = 227197811615775.
Find C(1013, 1012, 104) mod 999999937.
多项式相除的余数
对于正整数n和m，我们分别定义多项式 Fn(x) = xn和Gm(x) = (x-1)m。
另外，我们再定义多项式Rn,m(x)为多项式Fn(x)除以多项式Gm(x)的余数。
例如，R6,3(x) = 15x2 - 24x + 10。
记C(n, m, d)是Rn,m(x)中d次项系数的绝对值。
我们可以验证C(6, 3, 1) = 24，C(100, 10, 4) = 227197811615775。
求C(1013, 1012, 104) mod 999999937。