[{"sectionTitle":"题目描述","type":"Text","text":"佳佳碰到了一个难题，请你来帮忙解决。对于不定方程 $a_1+a_2+\\cdots +a_{k-1}+a_k=g(x)$，其中 $k\\ge 2$ 且 $k\\in \\mathbb{N}^*$，$x$ 是正整数，$g(x)=x^x \\bmod 1000$（即 $x^x$ 除以 $1000$ 的余数），$x,k$ 是给定的数。我们要求的是这个不定方程的正整数解组数。\r\n\r\n举例来说，当 $k=3,x=2$ 时，方程的解分别为：\r\n$$\r\n\begin{cases}\r\na_1=1\\\r\na_2=1\\\r\na_3=2\r\n\end{cases}\r\n \ \ \ \\r\n\begin{cases}\r\na_1=1\\\r\na_2=2\\\r\na_3=1\r\n\end{cases}\r\n \ \ \ \\r\n\begin{cases}\r\na_1=2\\\r\na_2=1\\\r\na_3=1\r\n\end{cases}\r\n$$\r\n","subType":"markdown"},{"sectionTitle":"输入格式","type":"Text","text":"有且只有一行，为用空格隔开的两个正整数，依次为 $k,x$。","subType":"markdown"},{"sectionTitle":"输出格式","type":"Text","text":"有且只有一行，为方程的正整数解组数。","subType":"markdown"},{"sectionTitle":"样例","type":"Sample","text":"","subType":"markdown","payload":["3 2","3"]},{"sectionTitle":"数据范围与提示","type":"Text","text":"对于 $40\\%$ 数据，答案不超过 $10^{16}$； \r\n对于全部数据，$1\\le k\\le 100,1\\le x\\lt 2^{31},k\\le g(x)$。","subType":"markdown"}]