<p>You have <code>k</code> lists of sorted integers in <strong>non-decreasing&nbsp;order</strong>. Find the <b>smallest</b> range that includes at least one number from each of the <code>k</code> lists.</p>

<p>We define the range <code>[a, b]</code> is smaller than range <code>[c, d]</code> if <code>b - a &lt; d - c</code> <strong>or</strong> <code>a &lt; c</code> if <code>b - a == d - c</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [[4,10,15,24,26],[0,9,12,20],[5,18,22,30]]
<strong>Output:</strong> [20,24]
<strong>Explanation: </strong>
List 1: [4, 10, 15, 24,26], 24 is in range [20,24].
List 2: [0, 9, 12, 20], 20 is in range [20,24].
List 3: [5, 18, 22, 30], 22 is in range [20,24].
</pre>

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

<pre>
<strong>Input:</strong> nums = [[1,2,3],[1,2,3],[1,2,3]]
<strong>Output:</strong> [1,1]
</pre>

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

<ul>
	<li><code>nums.length == k</code></li>
	<li><code>1 &lt;= k &lt;= 3500</code></li>
	<li><code>1 &lt;= nums[i].length &lt;= 50</code></li>
	<li><code>-10<sup>5</sup> &lt;= nums[i][j] &lt;= 10<sup>5</sup></code></li>
	<li><code>nums[i]</code>&nbsp;is sorted in <strong>non-decreasing</strong> order.</li>
</ul>

class Answer:
    def __init__(self, left, right):
        self.left = left
        self.right = right
    def __lt__(self, other):
        a = self.right - self.left
        b = other.right - other.left
        return a < b or (a == b and self.left < other.left) 

class Solution:
    def smallestRange(self, nums: List[List[int]]) -> List[int]:
        h = [(nums[i][0], i, 0) for i in range(len(nums))]
        heapify(h)
        merged = []
        while h:
            val, i, j = heappop(h)
            merged.append((val, i))
            j += 1
            if j < len(nums[i]):
                heappush(h, (nums[i][j], i, j))
        i = 0
        j = 0
        t = 0
        counter = defaultdict(int)
        ans = Answer(merged[0][0], merged[-1][0])
        while i < len(merged):
            while j < len(merged) and t < len(nums):
                val, row = merged[j]
                counter[row] += 1
                if counter[row] == 1:
                    t += 1
                j += 1
            if t == len(nums):
                ans = min(ans, Answer(merged[i][0], merged[j-1][0]))
            counter[merged[i][1]] -= 1
            if counter[merged[i][1]] == 0:
                t -= 1
            i += 1
        return [ans.left, ans.right]

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