Minimum Segments

You are given closed intervals and may add exactly one extra closed interval with length b−a≤k. Find the minimum number of connected blocks after merging. Touching at the same endpoint counts as connected; intervals that differ by 1 are not automatically connected.

输入格式

The first line contains n k, followed by n lines of a b. 1≤n≤200000, 1≤a≤b≤10⁹, 1≤k≤10⁹. The added interval may have length 0.

输出格式

Output the single integer required by the problem.

样例 1

输入：

4 2
1 2
2 4
5 8
10 11

输出：

2

样例 2

输入：

2 1
1 1
2 2

输出：

1

样例 3

输入：

1 1
1 100

输出：

1

样例说明

The answers to the three public examples are, in order: 2; 1; 1. The examples were rechecked by independent enumeration, state search, or direct simulation.