Sherlock and Watson are playing a game. The game is as follows:
There are n cards in order on the table. Each card has some single digit number written on it. Sherlock asks Watson to form all ordered subsequences of the n cards and answer with the total of all the numbers obtained by each of the subsequence.
For example if cards are numbered as 1,2 and 3 in order. The subsequences obtained are: 1, 2, 3, 12, 13, 23, 123. Sum of the numbers of subsequence is = 1+2+3+12+13+23+123 = 177.
As the output can be large, output it modulo $$10^9 + 7$$
Watson is not so proficient at math and asks for your help.
First line contains T : number of test cases. T lines follow, each containing a number having N digits. It is guaranteed that the first card will not have number 0 written on it.
A number containing the sum of numbers obtained by each ordered subsequence.
$$ 1<= T <= 10 $$
$$ 1<= N <= 2*10^5 $$ ( N is number of digits in given number)
Setter : Karan Thakkar
The subsequence of number 123 are 123, 12 , 23, 13, 1, 2 and 3. Whose sum is 177.
The subsequence of number 111 are 111, 11 , 11, 11, 1, 1 and 1. Whose sum is 147.