<p>Given an integer array <code>nums</code>, return the sum of <code>floor(nums[i] / nums[j])</code> for all pairs of indices <code>0 &lt;= i, j &lt; nums.length</code> in the array. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>The <code>floor()</code> function returns the integer part of the division.</p>

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

<pre>
<strong>Input:</strong> nums = [2,5,9]
<strong>Output:</strong> 10
<strong>Explanation:</strong>
floor(2 / 5) = floor(2 / 9) = floor(5 / 9) = 0
floor(2 / 2) = floor(5 / 5) = floor(9 / 9) = 1
floor(5 / 2) = 2
floor(9 / 2) = 4
floor(9 / 5) = 1
We calculate the floor of the division for every pair of indices in the array then sum them up.
</pre>

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

<pre>
<strong>Input:</strong> nums = [7,7,7,7,7,7,7]
<strong>Output:</strong> 49
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def sumOfFlooredPairs(self, nums: List[int]) -> int:
        max_num = max(nums)
        frequencies = [0] * (max_num + 1)
        for num in nums:
            frequencies[num] += 1

        freqs_prefix_sums = []
        for frequency in frequencies:
            if not freqs_prefix_sums:
                freqs_prefix_sums.append(frequency)
                continue
            freqs_prefix_sums.append(freqs_prefix_sums[-1] + frequency)

        total_sum, unique_nums = 0, set(nums)
        for num in unique_nums:
            for multiple in range(1, max_num // num + 1):
                # Starting from multiple * num to min of (multiple + 1) * num - 1 and max num.
                total_frequencies = freqs_prefix_sums[min((multiple + 1) * num - 1, max_num)]
                total_frequencies -= freqs_prefix_sums[multiple * num - 1]
                total_sum += multiple * frequencies[num] * total_frequencies
        
        return total_sum % (10 ** 9 + 7)

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