You are given an integer array nums and an integer k.

Starting with an initial value of $1$, you iterate through each element in nums from left to right. For each element nums[i], you must perform exactly one of the following operations on the current value:

• Multiply the value by nums[i]

• Divide the value by nums[i]

• Leave the value unchanged

Return the total number of distinct sequences of choices that result in a final value equal to k.

Constraints:

• $1 \leq$ nums.length $\leq 19$

• $1 \leq$ nums[i] $\leq 6$

• $1 \leq$ k $\leq 10^{15}$

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.