Problem J
Parovi
The distance between two integers is defined as the sum of the absolute result of subtracting their digits. For example, the distance between the numbers 4561 and 3278 is $|4 - 3| + |5 - 2| + |6 - 7| + |1 - 8| = 12$. If one of the numbers consists of fewer digits than the other, we fill it with leading zeroes. Therefore, the distance between the numbers 32 and 5678 is $|0 - 5| + |0 - 6| + |3 - 7| + |2 - 8| = 21$. You are given two integers $A$ and $B$. Calculate the sum of distances between each pair of numbers belonging in the interval $[A, B]$.
Input
The first and only line of input contains integers $A$, $B$ ($1 \leq A \leq B \leq 10^{50\, 000}$).
Output
The first and only line of output must contain the required number from the text. Given that the number could be extremely large, output the answer modulo $1\, 000\, 000\, 007$.
| Sample Input 1 | Sample Output 1 |
|---|---|
1 5 |
40 |
| Sample Input 2 | Sample Output 2 |
|---|---|
288 291 |
76 |
| Sample Input 3 | Sample Output 3 |
|---|---|
1000000 10000000 |
581093400 |