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 $N$ 头牛按照她们必须出现在舞蹈中的顺序方便地编号为 $1,2,...N$。第 $i$ 头牛计划跳 $d_i$ 的特定持续时间。 一开始，第 $1,2,...K$ 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。

接下来的 $N$ 行，第 $i$ 行给出了第 $i$ 头牛跳舞的持续时间 $d_i$。第 $i$ 行包括一个整数 $d_i$。

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。

样例 #1

样例输入 #1

5 8
4
7
8
6
4

样例输出 #1

4

提示

于 $100\%$ 的数据，$1 \le N \le 10^4$，$T_{max} \le 10^6$，$1 \le d_i \le 10^5$。