A902. Cow Dance Show--Silver

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 $K$.

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.

Print out the smallest possible value of $K$ such that the dance performance
will take no more than $T_{max}$ units of time.