一、题目

You are given positive integers n and target.

An array nums is beautiful if it meets the following conditions:

nums.length == n.
nums consists of pairwise distinct positive integers.
There doesn’t exist two distinct indices, i and j, in the range [0, n - 1], such that nums[i] + nums[j] == target.
Return the minimum possible sum that a beautiful array could have modulo 109 + 7.

Example 1:

Input: n = 2, target = 3
Output: 4
Explanation: We can see that nums = [1,3] is beautiful.

• The array nums has length n = 2.
• The array nums consists of pairwise distinct positive integers.
• There doesn’t exist two distinct indices, i and j, with nums[i] + nums[j] == 3.
  It can be proven that 4 is the minimum possible sum that a beautiful array could have.
  Example 2:

Input: n = 3, target = 3
Output: 8
Explanation: We can see that nums = [1,3,4] is beautiful.

• The array nums has length n = 3.
• The array nums consists of pairwise distinct positive integers.
• There doesn’t exist two distinct indices, i and j, with nums[i] + nums[j] == 3.
  It can be proven that 8 is the minimum possible sum that a beautiful array could have.
  Example 3:

Input: n = 1, target = 1
Output: 1
Explanation: We can see, that nums = [1] is beautiful.

Constraints:

1 <= n <= 109
1 <= target <= 109

二、题解

class Solution {
public:int minimumPossibleSum(int n, int target) {int mod = 1e9 + 7;long long m = min(target / 2, n);return (m * (m + 1) + (n - m - 1 + 2 * target) * (n - m)) / 2 % mod;}
};