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# Find K Pairs with Smallest Sums

You are given two integer arrays **nums1** and **nums2** sorted in ascending order and an integer **k**.

Define a pair **(u,v)** which consists of one element from the first array and one element from the second array.

Find the k pairs **(u1,v1),(u2,v2) ...(uk,vk)** with the smallest sums.

**Example 1:**

```
Input: nums1 = [1,7,11], nums2 = [2,4,6], k = 3
Output: [[1,2],[1,4],[1,6]] 
Explanation: The first 3 pairs are returned from the sequence: 
             [1,2],[1,4],[1,6],[7,2],[7,4],[11,2],[7,6],[11,4],[11,6]
```

**Example 2:**

```
Input: nums1 = [1,1,2], nums2 = [1,2,3], k = 2
Output: [1,1],[1,1]
Explanation: The first 2 pairs are returned from the sequence: 
             [1,1],[1,1],[1,2],[2,1],[1,2],[2,2],[1,3],[1,3],[2,3]
```

**Example 3:**

```
Input: nums1 = [1,2], nums2 = [3], k = 3
Output: [1,3],[2,3]
Explanation: All possible pairs are returned from the sequence: [1,3],[2,3]
```

```java
class Solution {
    public List<List<Integer>> kSmallestPairs(int[] nums1, int[] nums2, int k) {
        int nlen1 = nums1.length, nlen2 = nums2.length;
        List<List<Integer>> res = new ArrayList<>();
        if (nlen1 == 0 || nlen2 == 0 || k == 0)
            return res;
        PriorityQueue<List<Integer>> pq = new PriorityQueue<>((a, b) -> a.get(0) + a.get(1) - b.get(0) - b.get(1));
        for (int i = 0; i < nums1.length && i < k; i++) {
            List<Integer> pair = new ArrayList<>();
            pair.addAll(Arrays.asList(nums1[i], nums2[0], 0));
            pq.add(pair);
        }
        while (k-- > 0 && !pq.isEmpty()) {
            List<Integer> cur = pq.poll();
            res.add(Arrays.asList(cur.get(0), cur.get(1)));
            // reach end of nums2
            if (cur.get(2) == nums2.length - 1)
                continue;
            List<Integer> p2 = new ArrayList<>();
            p2.addAll(Arrays.asList(cur.get(0), nums2[cur.get(2) + 1], cur.get(2) + 1));
            pq.add(p2);
        }
        return res;
    }
}
```


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