You are trying to improve your competitive programming skills and you have listed all the problems along with their difficulty level. You have to plan your schedule in order to maximize your skills.

You are given an integer array difficultyLevel$[]$ of size N denoting the difficulty levels of N problems listed. You are provided with an integer K denoting the exact number of problems you can solve in a day. The skill you achieve after solving all the problems is defined as the summation of the products of the difficulty levels of all the problems solved each day.

Your task is to design a schedule that can maximize your skill at the end of this exercise and return the maximum skill you can attain. As the answer is too large, return the answer modulus $10^9+7.$

Note: Before multiplying the difficulty levels of two integers A and B$,$ you need to reduce each integer to $($A$\%10^9+7)$ and $($B $\%10^9+7).$

Input Specification:

input$1$: an integer array denoting difficultyLevel$[]$

input$2$: an integer N denoting the length of the array difficultyLevel$[]$

input$3$: an integer K denoting the exact number of problems you can solve each day.

Output Specification:

An integer denoting the maximum skill you can attain.

Example $1$:

input$1$: $[10,12,2,5,1,9]$

input$2$: $6$

input$3$: $2$

Output: $167$

Explanation:

The value of mod $1000000007$ i$.$e $10^9+7.$

On day $1,$ we can solve problems with difficulty levels $10$ and $12.$ Thus the product is $((10)\%$mod$)*((12)\%$mod$)=120$ refer to Note above

$$ On day $2,$ we can solve problems with difficulty levels $5$ and $9.$ Thus the product. is $((5)\%$mod$)((9)\%$mod$)=45.$

$$ On day $3,$ we can solve problems with difficulty levels $2$ and $1.$ Thus the product is $=((2)\%$mod$)*((1)\%$mod$)=2.$

The summation of the products of the difficulty levels of all the problems solved each day $=2+45+120=167$ and $(167\%$ mod$)=167.$ This is the maximum possible skill that can be achieved. Therefore, $167$ will be returned as the answer.

Example $2$:

input$1$: $[2,10,50,32]$

input$2$: $4$

input$3$: $2$

Output: $1620$

Explanation:

$$ On day $1,$ we can solve problems with difficulty levels $2$ and $10.$ Thus the product is $((2)\%$mod$)*((10)\%$mod$)=20.$

$$ On day $2,$ we can solve problems with difficulty levels $32$ and $50.$ Thus the product is $((32)\%$mod$)*((50)\%$mod$)=1600.$

The summation of the products of the difficulty levels of all the problems solved each day $=20+1600=1620$ and $(1620\%$ mod$)=1620.$ This is the maximum possible skill that can be achieved. write a c$++$ code