Some robots are placed on a $1$ dimensional line. You are given a $0$ indexed integer array nums, a string s, and an integer d.

The robot at index i is initially positioned at nums[i] and begins moving in the direction indicated by s[i]. If s[i] is 'L', the robot moves to the left, and if s[i] is 'R', it moves to the right.

Every second, all robots move $1$ unit in their current direction. If two robots collide at the same position, both instantly reverse their directions and keep moving.

Return the sum of the distances between all pairs of robots after $d$ seconds. Since the sum can be large, return it modulo $10^9 + 7$.

Note:
Robots change direction instantly upon collision without any loss of time. Collisions occur only when robots meet at the exact same position.

Constraints:

• $2 \le$ nums.length $\le 10^5$

• $-2 imes 10^9 \le$ nums[i] $\le 2 imes 10^9$

• $0 \le$ d $\le 10^9$

• nums.length $==$ s.length

• s consists of 'L' and 'R' only

• All elements in nums are unique

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.