You have a number of envelopes with widths and heights given as a pair of integers (w, h). One envelope can fit into another if and only if both the width and height of one envelope is greater than the width and height of the other envelope.

What is the maximum number of envelopes can you Russian doll? (put one inside other)

Note: Rotation is not allowed.

Example:

Input: [[5,4],[6,4],[6,7],[2,3]]

Output: 3

Explanation: The maximum number of envelopes you can Russian doll is 3 ([2,3] => [5,4] => [6,7]).

You are given K eggs, and you have access to a building with N floors from 1 to N.

Each egg is identical in function, and if an egg breaks, you cannot drop it again.

You know that there exists a floor F with 0 <= F <= N such that any egg dropped at a floor higher than F will break, and any egg dropped at or below floor F will not break.

Each move, you may take an egg (if you have an unbroken one) and drop it from any floor X (with 1 <= X <= N).

Your goal is to know with certainty what the value of F is.

What is the minimum number of moves that you need to know with certainty what F is, regardless of the initial value of F?

Example 1:

Input: K = 1, N = 2

Output: 2

Explanation: Drop the egg from floor 1. If it breaks, we know with certainty that F = 0.

Otherwise, drop the egg from floor 2. If it breaks, we know with certainty that F = 1.

If it didn't break, then we know with certainty F = 2.

Hence, we needed 2 moves in the worst case to know what F is with certainty.

Example 2:

Input: K = 2, N = 6

Output: 3

Example 3:

Input: K = 3, N = 14

Output: 4

Note:

1 <= K <= 100

1 <= N <= 10000