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 \(f_1-f_2+f_3-f_4+\cdots+(-1)^{j+1}f_j\).

(第十八届AIME2 2000 第14题)