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 $A$, $B$ ($1 \leq A \leq B \leq 10^{50000}$).

-----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 $1000000007$.

-----Examples-----
Sample Input 1:
1 5
Sample Output 1:
40

Sample Input 2:
288 291
Sample Output 2:
76

Source: kattis | Difficulty: HARD


Solutions: