Solve the programming task below in a Python markdown code block.
A number, ${x}$, is called irresponsible when adding ${x}$ to $x+1$ requires a carry operation. For example, $5$, $17$, and ${91}$ are irresponsible numbers because adding them to ${6}$, ${18}$, and $92$ (respectively) requires a carry operation:

In $5+(5+1)=5+6=11$, a ${1}$ is carried over into the $10$'s place. 
In $17+(17+1)=17+18=35$, a $2$ is carried over into the $10$'s place.
In $91+(91+1)=91+92=183$, a ${1}$ is carried over into the $\left(\begin{array}{c c}{{1}}&{{0}}&{{0}}\\ {{0}}&{{0}}&{{0}}\\ {{0}}&{{0}}&{{0}}&{{0}}\\ {{0}}&{{0}}&{{0}}&{{0}}\\ {{0}}&{{0}}&{{0}}&{{0}}\\ {{0}}&{{0}}&{{0}}&{{0}}\\ {{0}}&{{0}}&{{0}}&{{0}}\\ \end{array}\right).$'s place.

You have two integers, ${x}$ and $n$. Construct a new number, ${s}$, by repeating ${x}$ a total of $n$ times. For example, if $x=3121$ and $n=4$, then $s=3121312131213121$.

Given ${x}$ and $n$, construct ${s}$ and find all the irreponsible numbers between ${1}$ and ${s}$. Then print the number of irresponsible numbers in the aforementioned range; as this number can be quite large, your answer must be modulo $10^9+7$.

Input Format

A single line with two space-separated integers denoting the respective values of ${x}$ and $n$.

Constraints

$1\leq x\leq10^{1,000,000}$
$1\leq n\leq10^{18}$

Subtasks

For $15\%$ of the maximum score: 

$1\leq x\leq10^{6}$
$n=1$

For ${40\%}$ of the maximum score: 

$1\leq x\leq10^{1,000,000}$
$n=1$

Output Format

Print a single integer denoting the number of irresponsible numbers between ${1}$ and ${s}$, modulo $10^9+7$.

Sample Input
1 2

Sample Output
4

Explanation

When we repeat $x=1$ a total of $n=2$ times we get ${11}$. The irresponsible numbers between ${1}$ and ${11}$ are $5$, ${6}$, $7$, and $8$. Because there are four irresponsible numbers, we print $4\times(10^9+7)=4$ on a new line.