题目简要描述
设num[i]表示既是S[1..i]的前缀又是后缀，并且前缀和后缀不重叠的字符串个数。
求$\prod_{i=1}^n (num[i]+1)=(num[1]+1)\times (num[2]+1)\times \dots \times (num[n]+1)$对$1000000007$取模的结果。
10%:|S|<=50
30%:|S|<=200
50%:|S|<=10000
100%:|S|<=1000000
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