<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 Solution {
public:
    vector<int> smallestRange(vector<vector<int>>& nums) {
        vector<int>ans;
        int k = nums.size();

        int num1 = INT_MIN;
        int num2 = INT_MIN;

        set<int>visited;
        
        for(int i=0; i<k; i++) {
            for(int j=0; j<nums[i].size(); j++) {
                bool impossible = false;
                int lower = nums[i][j];
                if(visited.find(lower) != visited.end()) continue;
                visited.insert(lower);

                int upper = lower;

                for(int prev = 0; prev < k; prev++) {
                    if(prev == i) continue;

                    auto it = lower_bound(nums[prev].begin(), nums[prev].end(), lower);
                    if(it == nums[prev].end()) { //all elements are smaller
                        impossible = true;
                        continue;
                    }
                    
                    if(*it == lower) continue;

                    upper = max(upper, *it);
                }

                if(impossible) continue;


                if(num1 == INT_MIN && num2 == INT_MIN) {
                    num1 = lower;
                    num2 = upper;
                }
                else {
                    if(abs(upper-lower) < abs(num1-num2)) {
                        num1 = lower;
                        num2 = upper;
                    }
                    else if(abs(upper-lower) == abs(num1-num2) && lower < num1) {
                        num1 = lower;
                        num2 = upper;
                    }
                }
            }
        }

        ans.push_back(num1);
        ans.push_back(num2);

        return ans;
    }
};
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