[USACO12MAR]花盆Flowerpot

题目描述

Farmer John has been having trouble making his plants grow, and needs your help to water them properly. You are given the locations of N raindrops (1 <= N <= 100,000) in the 2D plane, where y represents vertical height of the drop, and x represents its location over a 1D number line: ![](https://cdn.luogu.com.cn/upload/pic/9174.png) Each drop falls downward (towards the x axis) at a rate of 1 unit per second. You would like to place Farmer John's flowerpot of width W somewhere along the x axis so that the difference in time between the first raindrop to hit the flowerpot and the last raindrop to hit the flowerpot is at least some amount D (so that the flowers in the pot receive plenty of water). A drop of water that lands just on the edge of the flowerpot counts as hitting the flowerpot. Given the value of D and the locations of the N raindrops, please compute the minimum possible value of W. 老板需要你帮忙浇花。给出N滴水的坐标,y表示水滴的高度,x表示它下落到x轴的位置。 每滴水以每秒1个单位长度的速度下落。你需要把花盆放在x轴上的某个位置,使得从被花盆接着的第1滴水开始,到被花盆接着的最后1滴水结束,之间的时间差至少为D。 我们认为,只要水滴落到x轴上,与花盆的边沿对齐,就认为被接住。给出N滴水的坐标和D的大小,请算出最小的花盆的宽度W。

输入输出格式

输入格式


第一行2个整数 N 和 D。 第2.. N+1行每行2个整数,表示水滴的坐标(x,y)。

输出格式


仅一行1个整数,表示最小的花盆的宽度。如果无法构造出足够宽的花盆,使得在D单位的时间接住满足要求的水滴,则输出-1。

输入输出样例

输入样例 #1

4 5
6 3
2 4
4 10
12 15

输出样例 #1

2

说明

【样例解释】 有4滴水, (6,3), (2,4), (4,10), (12,15).水滴必须用至少5秒时间落入花盆。花盆的宽度为2是必须且足够的。把花盆放在x=4..6的位置,它可以接到1和3水滴, 之间的时间差为10-3 = 7满足条件。 【数据范围】 40%的数据:1 ≤ N ≤ 1000,1 ≤ D ≤ 2000; 100%的数据:1 ≤ N ≤ 100000,1 ≤ D ≤ 1000000,0≤x,y≤10^6。