PAROVI

문제

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. 

힌트

The distances are, respectively, (288, 289) = 1, (288, 290) = 9, (288, 291) = 8, (289, 290) = 10, (289, 291) = 9, (290, 291) = 1. Each of them counts twice, which is in total 2 * (1 + 9 + 8 + 10 + 9 +1) = 76. 

1 5

40

288 291

76

1000000 10000000

581093400