Description

You have k identical eggs and n floors. Find the minimum number of moves needed to determine with certainty what the critical floor f is (the minimum floor from which an egg breaks when dropped).

Examples

Input:k = 2, n = 6
Output:3
Explanation:

With 2 eggs and 6 floors, minimum 3 moves needed.

Input:k = 1, n = 10
Output:10
Explanation:

With only 1 egg and 10 floors, a linear search strategy starting from floor 1 is required. In the worst case, the critical floor is floor 10, requiring testing floors 1, 2, 3, ..., 10 sequentially. This takes 10 moves.

Input:k = 4, n = 8
Output:4
Explanation:

With 4 eggs and 8 floors, an efficient binary-search-like strategy works. Starting by dropping from floor 4: if it breaks, 3 eggs remain for floors 1-3 (at most 3 moves). If it does not break, floor 6 is tested next. This strategy guarantees finding the critical floor in 4 moves.

Constraints

  • 1 ≤ k ≤ 100
  • 1 ≤ n ≤ 10⁴

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