题目描述
<p class="MsoNormal" style="line-height: 21pt; margin: 0cm 0cm 0pt; mso-line-height-rule: exactly"><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对于不定方程</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">a<sub>1</sub>+a<sub>2</sub>+</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">……</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">+a<sub>k-1</sub>+a<sub>k</sub>=g(x)</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，其中</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">k>=2</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">且</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">k</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">是自然数，</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">x</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">是正整数，</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">g(x)=x<sup>x</sup> mod 1000</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">x</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">、</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">k</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">是给定的数。我们要求的是这个不定方程的正整数解的组数。</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></span></p> <p class="MsoNormal" style="line-height: 21pt; margin: 0cm 0cm 0pt; mso-line-height-rule: exactly"><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">举例来说，当</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">k=3</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">x=2</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">时，</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">g(x)=4</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，原方程即</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">a<sub>1</sub>+a<sub>2</sub>+a<sub>3</sub>=4</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></span></p> <p class="MsoNormal" style="line-height: 21pt; margin: 0cm 0cm 0pt; mso-line-height-rule: exactly"><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">这个方程的正整数解有</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">3</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">组，分别为（</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">a<sub>1</sub>,a<sub>2</sub>,a<sub>3</sub></font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">）</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">=(2,1,1),(1,2,1),(1,1,2)</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">；</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></span></p> <p></p>
输入格式
<p class="MsoNormal" style="line-height: 21pt; margin: 0cm 0cm 0pt; mso-line-height-rule: exactly"><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">只有一行，为用空格隔开的两个正整数，依次为</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">k</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><font face="Times New Roman">x</font></span><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></span></p>
输出格式
<p class="MsoNormal" style="line-height: 21pt; margin: 0cm 0cm 0pt; mso-line-height-rule: exactly"><span style="font-family: 宋体; font-size: 12pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">只有一行，为方程的正整数解的组数。</span><span lang="EN-US" style="font-size: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></span></p>
样例
样例输入 1
3 2
样例输出 1
3
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