题目描述
After several months of rehearsal, the cows are just about ready to put on their annual dance performance; this year they are performing the famous bovine ballet "Cowpelia".
The only aspect of the show that remains to be determined is the size of the stage. A stage of size $K$ can support $K$ cows dancing simultaneously. The $N$ cows in the herd ($1 \"leq N \"leq 10,000$) are conveniently numbered $1 \"ldots N$ in the order in which they must appear in the dance. Each cow $i$ plans to dance for a specific duration of time $d(i)$. Initially, cows $1 \"ldots K$ appear on stage and start dancing. When the first of these cows completes her part, she leaves the stage and cow $K+1$ immediately starts dancing, and so on, so there are always $K$ cows dancing (until the end of the show, when we start to run out of cows). The show ends when the last cow completes her dancing part, at time $T$.
Clearly, the larger the value of $K$, the smaller the value of $T$. Since the show cannot last too long, you are given as input an upper bound $T_{max}$ specifying the largest possible value of $T$. Subject to this constraint, please determine the smallest possible value of $K$.
经过几个月的排练,奶牛们基本准备好展出她们的年度舞蹈表演。今年她们要表演的是著名的奶牛芭蕾——“cowpelia”。
表演唯一有待决定的是舞台的尺寸。一个大小为K的舞台可以支持K头牛同时在舞台上跳舞。在牛群中的N头牛(1<=N<=10,000)按照她们必须出现在舞蹈中的顺序方便地编号为1..N。第i头牛计划跳d[i]的特定持续时间。一开始,第1..K头牛出现在舞台上并开始跳舞。当这些牛中的某一头牛首先完成了她的部分,她会马上离开舞台并且第K+1头牛会出现在舞台上并开始跳舞。所以,舞台上总有K头奶牛在跳舞(直到表演的尾声,奶牛不够的时候)。当最后一头奶牛完成了她的舞蹈部分,表演结束,共花了T个单位时间。
显然,K的值越大,T就越小。由于表演不能拖太长,你得知了指定T的最大可能值的上限T-max。请根据这个约束,确定K的最小值。
输入格式:
The first line of input contains $N$ and $T_{max}$, where $T_{max}$ is an integer of value at most 1 million.
The next $N$ lines give the durations $d(1) \"ldots d(N)$ of the dancing parts for cows $1 \"ldots N$. Each $d(i)$ value is an integer in the range $1 \"ldots 100,000$.
It is guaranteed that if $K=N$, the show will finish in time.
第一行包括N和T-max两个整数(T-max<=1,000,000)。
接下来的N行给出了第1..n头牛跳舞的持续时间d[1]..d[n]。第i行包括一个整数d[i],1<=d[i]<=100,000.
保证K=N时表演会按时完成。
输出格式:
Print out the smallest possible value of $K$ such that the dance performance will take no more than $T_{max}$ units of time.
输出在表演时间不大于T-max时的K的最小可能值。
输入样例#1:
5 8
4
7
8
6
4
输出样例#1:
4