<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <em>the number of <strong>subarrays</strong> of </em><code>nums</code><em> where the least common multiple of the subarray&#39;s elements is </em><code>k</code>.</p>

<p>A <strong>subarray</strong> is a contiguous non-empty sequence of elements within an array.</p>

<p>The <strong>least common multiple of an array</strong> is the smallest positive integer that is divisible by all the array elements.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,6,2,7,1], k = 6
<strong>Output:</strong> 4
<strong>Explanation:</strong> The subarrays of nums where 6 is the least common multiple of all the subarray&#39;s elements are:
- [<u><strong>3</strong></u>,<u><strong>6</strong></u>,2,7,1]
- [<u><strong>3</strong></u>,<u><strong>6</strong></u>,<u><strong>2</strong></u>,7,1]
- [3,<u><strong>6</strong></u>,2,7,1]
- [3,<u><strong>6</strong></u>,<u><strong>2</strong></u>,7,1]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [3], k = 2
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no subarrays of nums where 2 is the least common multiple of all the subarray&#39;s elements.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i], k &lt;= 1000</code></li>
</ul>

class Solution:
    def subarrayLCM(self, nums: List[int], k: int) -> int:
        primes = list(range(2,1001))
        for i in primes:        #now primes contain only the primes
            for j in range(2,1001//i+1):
                if i*j in primes:
                    primes.remove(i*j)
        def decomp(t):
            s = set()
            for p in primes:
                maxp = 1
                if t == 1:
                    break
                while t%p == 0:
                    maxp = maxp*p
                    t = t//p
                s.add(maxp)
            s.discard(1)
            return s
        if nums == []: #excludes the case where nothing divides k
            return 0
        decompk = decomp(k)
        if any(k%n != 0 for n in nums):  #reduces to lists where everything divides k
            ls = [[]]
            for n in nums:
                if k % n == 0:
                    ls[-1].append(n)
                elif ls[-1] == []:
                    continue
                else:
                    ls.append([])
            return sum(self.subarrayLCM(u,k) for u in ls)  
        if k == 1: #excludes the case where k = 1
            return (len(nums)*(len(nums)+1))//2      
        newnums = []
        for x in nums:
            newnums.append(decomp(x))
        start = 0
        ans = 0
        n = len(nums)
        while start < n:
            end = start
            u = decompk
            v = newnums[start]
            while end < n:
                v = v | newnums[end]
                if not u.issubset(v) and end != n-1:
                    end += 1
                    continue
                if not u.issubset(v) and end == n-1:
                    start +=1
                    break
                ans += (n - end)
                start += 1
                break
        return ans
640