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 Specification

The first and only line of input contains integers ~A~, ~B~ ~(1 \le A \le B \le 10^{50\,000})~.

Output Specification

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~.

Scoring

In test cases worth ~20\%~ of total points, ~A~ and ~B~ will not exceed ~10\,000~.

In test cases worth ~40\%~ of total points, ~A~ and ~B~ will not exceed ~10^{100}~.

Sample Input 1

1 5

Sample Output 1

40

Sample Input 2

288 291

Sample Output 2

76

Explanation for Sample Output 2

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 \times (1+9+8+10+9+1) = 76~.

Sample Input 3

1000000 10000000

Sample Output 3

581093400