[USACO08OPEN] Cow Cars S

题目描述

N (1 <= N <= 50,000) cows conveniently numbered 1..N are driving in separate cars along a highway in Cowtopia. Cow i can drive in any of M different high lanes (1 <= M <= N) and can travel at a maximum speed of S_i (1 <= S_i <= 1,000,000) km/hour.

After their other bad driving experience, the cows hate collisions and take extraordinary measures to avoid them. On this highway, cow i reduces its speed by D (0 <= D <= 5,000) km/hour for each cow in front of it on the highway (though never below 0 km/hour). Thus, if there are K cows in front of cow i, the cow will travel at a speed of max[S_i - D * K, 0]. While a cow might actually travel faster than a cow directly in front of it, the cows are spaced far enough apart so crashes will not occur once cows slow down as

described,

Cowtopia has a minimum speed law which requires everyone on the highway to travel at a a minimum speed of L (1 <= L <= 1,000,000) km/hour so sometimes some of the cows will be unable to take the highway if they follow the rules above. Write a program that will find the maximum number of cows that can drive on the highway while obeying the minimum speed limit law.

编号为 $1$ 到 $N$ 的 $N$ 只奶牛正各自驾着车打算在牛德比亚的高速公路上飞驰．高速公路有 $M(1\leq M\leq N)$ 条车道．奶牛 $i$ 有一个自己的车速上限$S_i(1\leq S_i\leq 10^6)$．

在经历过糟糕的驾驶事故之后，奶牛们变得十分小心，避免碰撞的发生．每条车道上，如果某一只奶牛 $i$ 的前面有 $k$ 只奶牛驾车行驶，那奶牛 $i$ 的速度上限就会下降 $k\times D$ 个单位，也就是说，她的速度不会超过 $S_i - k \times D(0\leq D\leq 5000)$，当然如果这个数是负的，那她的速度将是 $0$．牛德比亚的高速会路法规定，在高速公路上行驶的车辆时速不得低于$(1\leq L\leq 1,000,000)$．那么，请你计算有多少奶牛可以在高速公路上行驶呢？

输入格式

* Line 1: Four space-separated integers: N, M, D, and L

* Lines 2..N+1: Line i+1 describes cow i's initial speed with a single integer: S_i

输出格式

* Line 1: A single integer representing the maximum number of cows that can use the highway

样例 #1

样例输入 #1

3 1 1 5 
5 
7 
5

样例输出 #1

2

提示

There are three cows with one lane to drive on, a speed decrease of 1, and a minimum speed limit of 5.

Two cows are possible, by putting either cow with speed 5 first and the cow with speed 7 second.