2000 AIME II Problem 14

Every positive integer k has a unique factorial base expansion (f_1,f_2,f_3,\ldots,f_m), meaning that k=1!\cdot f_1+2!\cdot f_2+3!\cdot f_3+\cdots+m!\cdot f_m, where each f_i is an integer, 0\le f_i\le i, and 0<f_m. Given that (f_1,f_2,f_3,\ldots,f_j) is the factorial base expansion of 16!-32!+48!-64!+\cdots+1968!-1984!+2000!, find the value of f_1-f_2+f_3-f_4+\cdots+(-1)^{j+1}f_j.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.