Smallest Set Dodging a Sum

Medium

You are given two integers count and banned. Build a set of count distinct positive integers in which no two different elements add up to banned. Return the smallest possible sum of such a set.

Example 1

count=4, banned=6 → 12

Take 1, 2 and 3 (the 3 has no partner, since it appears only once); 4 and 5 would pair with 2 and 1 to make 6, so the fourth number is 6. The total is 1 + 2 + 3 + 6 = 12.

Example 2

count=3, banned=1 → 6

Two distinct positive integers never add up to 1, so 1, 2, 3 work.

Constraints

1 ≤ count ≤ 50
1 ≤ banned ≤ 50

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Topics

Greedy Math

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Input

count=4, banned=6

Expected

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