First to Count to Target

You are playing a game against a friend where in each round you pick a number from 1 to k to add to a shared running total that initially starts from 0. The first person to reach or exceed the running total to target wins.

Given that you go first, return whether you can force a win if everyone plays optimally.

Constraints

• k ≤ 30
• target ≤ 1,000

https://binarysearch.com/problems/First-to-Count-to-Target

Examples

Example 1

Input

• k = 5
• target = 9

Output

• answer = True

Explanation

If we pick 3 first, then whether your friend picks 1, 2, …, or 5 , we can always reach 9 by picking 5 next.

Example 2

Input

• k = 3
• target = 4

Output

• answer = False

Explanation

No mater what we pick your friend can pick 3 to reach 4.

Solution