Find K Pairs with Smallest Sums

You are given two integer arrays nums1 and nums2 sorted in non-decreasing 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.

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

Examples

Input: nums1 = [1,7,11], nums2 = [2,4,6], k = 3

Output: [[1,2],[1,4],[1,6]]

Explanation: The first 3 pairs with smallest sums are: (1,2), (1,4), (1,6). All of them use the smallest element from nums1.

Input: nums1 = [1,1,2], nums2 = [1,2,3], k = 2

Output: [[1,1],[1,1]]

Explanation: The first 2 pairs with smallest sums are: (1,1) and (1,1). Both pairs use elements from both arrays that sum to 2.

Input: nums1 = [1,2], nums2 = [3], k = 3

Output: [[1,3],[2,3]]

Explanation: All possible pairs are (1,3) and (2,3). Only 2 pairs exist, so we return both even though k = 3.

Constraints

• 1 <= nums1.length, nums2.length <= 10^5
• -10^9 <= nums1[i], nums2[i] <= 10^9
• nums1 and nums2 are sorted in non-decreasing order.
• 1 <= k <= 10^4
• k <= nums1.length * nums2.length