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:
Given nums1 = [1,7,11], nums2 = [2,4,6],  k = 3
Return: [1,2],[1,4],[1,6]
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:
Given nums1 = [1,1,2], nums2 = [1,2,3],  k = 2
Return: [1,1],[1,1]
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:
Given nums1 = [1,2], nums2 = [3],  k = 3 
Return: [1,3],[2,3]
All possible pairs are returned from the sequence:
[1,3],[2,3]
Credits:Special thanks to @elmirap and @StefanPochmann for adding this problem and creating all test cases.
class Solution:
     def kSmallestPairs(self, nums1, nums2, k):
         """
         :type nums1: List[int]
         :type nums2: List[int]
         :type k: int
         :rtype: List[List[int]]
         """
         queue = []
         def push(i, j):
             if i < len(nums1) and j < len(nums2):
                 heapq.heappush(queue, [nums1[i] + nums2[j], i, j])
         push(0, 0)
         pairs = []
         while queue and len(pairs) < k:
             _, i, j = heapq.heappop(queue)
             pairs.append([nums1[i], nums2[j]])
             push(i, j + 1)
             if j == 0:
                 push(i + 1, 0)
         return pairs
class Solution:
     def kSmallestPairs(self, nums1, nums2, k):
         """
         :type nums1: List[int]
         :type nums2: List[int]
         :type k: int
         :rtype: List[List[int]]
         """
         queue = []
         def push(i, j):
             if i < len(nums1) and j < len(nums2):
                 heapq.heappush(queue, [nums1[i] + nums2[j], i, j])
         push(0, 0)
         pairs = []
         while queue and len(pairs) < k:
             _, i, j = heapq.heappop(queue)
             pairs.append([nums1[i], nums2[j]])
             push(i, j + 1)
             if j == 0:
                 push(i + 1, 0)
         return pairs