There is an exam that contains n different types of questions. You are given an integer target and a $2 ext{D}$ integer array types where types[i] $= [ ext{count}_i, ext{marks}_i]$ indicates that there are $ ext{count}_i$ questions of the $i^{ ext{th}}$ type, and each question of that type awards $ ext{marks}_i$ points.

Return the total number of distinct ways to score exactly target points in the exam. Since the final answer may be very large, return it modulo $10^9 + 7$.

Note: Two ways are considered different if they differ in the number of questions solved for at least one type.

Constraints:

• $1 \leq$ target $\leq 1000$

• n $==$ types.length

• $1 \leq$ n $\leq 50$

• types[i].length $== 2$

• $1 \leq ext{count}_i, ext{marks}_i \leq 50$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.