P8245 [COCI 2013/2014 #3] PAROVI

Define the **distance** between two integers $A, B$ as the sum of the absolute differences of the digits in each corresponding position, denoted by $\operatorname{dist}(A,B)$. In particular, if $A$ and $B$ have different numbers of digits, pad the shorter one with leading zeros. For example: - $\operatorname{dist}(4561,3278)=\left|4-3\right|+\left|5-2\right|+\left|6-7\right|+\left|1-8\right|=12$. - $\operatorname{dist}(32,5678)=\left|0-5\right|+\left|0-6\right|+\left|3-7\right|+\left|2-8\right|=21$. Now, given two integers $L, R$, compute the sum of distances over all ordered pairs of integers within the interval $[L, R]$. Since the answer may be very large, **take it modulo $\bf 10^9+7$**.

The input consists of one line containing two integers $L, R$.

Output one integer per line: the sum of distances over all ordered pairs of integers in $[L, R]$, modulo $\bf 10^9+7$.

**[Sample 2 Explanation]** All distances between integer pairs in $[288,291]$ are: - $\operatorname{dist}(288,289)=\operatorname{dist}(289,288)=1$. - $\operatorname{dist}(288,290)=\operatorname{dist}(290,288)=9$. - $\operatorname{dist}(288,291)=\operatorname{dist}(291,288)=8$. - $\operatorname{dist}(289,290)=\operatorname{dist}(290,289)=10$. - $\operatorname{dist}(289,291)=\operatorname{dist}(291,289)=9$. - $\operatorname{dist}(290,291)=\operatorname{dist}(291,290)=1$. Therefore, the sum of distances is $2\times (1+9+8+10+9+1)=76$. **[Constraints and Limits]** For $20\%$ of the testdata, $A,B\leqslant 10^4$. For $40\%$ of the testdata, $A,B\leqslant 10^{100}$. For all testdata, $1\leqslant A\leqslant B\leqslant 10^{50000}$. **[Source]** This problem comes from **_[COCI 2013-2014](https://hsin.hr/coci/archive/2013_2014/) [CONTEST 3](https://hsin.hr/coci/archive/2013_2014/contest3_tasks.pdf) T5 PAROVI_**, and follows the original testdata settings, with a full score of $140$ points. Translated and整理 provided by [Eason_AC](https://www.luogu.com.cn/user/112917). Translated by ChatGPT 5