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

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 $1000000007$.

Scoring

In test cases worth $20\mathrm{\%}$ of total points, $A$ and $B$ will not exceed $10000$.

In test cases worth $40\mathrm{\%}$ 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