Find the Minimum Possible Sum of a Beautiful Array
You are given positive integers n and target.
You are given positive integers n and target.
An array nums is beautiful if it meets the following conditions:
Return the minimum possible sum that a beautiful array could have modulo 10^9 + 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 <= 10^9
- 1 <= target <= 10^9
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