문제

Author: Marin Tomić

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]!

입력

The first and only line of input contains integers A, B (1 ≤ A ≤ B ≤ 1050000).

출력

The first and only line of output must contain the required number from the text. Given that the number could be extremely large, output answer modulo 1 000 000 007.

예제 입력 1

1 5

예제 출력 1

40

예제 입력 2

288 291

예제 출력 2

76

예제 입력 3

1000000 10000000

예제 출력 3

581093400