CF1783C.Yet Another Tournament

You are participating in Yet Another Tournament. There are $n + 1$ participants: you and $n$ other opponents, numbered from $1$ to $n$.

Each two participants will play against each other exactly once. If the opponent $i$ plays against the opponent $j$, he wins if and only if $i \gt j$.

When the opponent $i$ plays against you, everything becomes a little bit complicated. In order to get a win against opponent $i$, you need to prepare for the match for at least $a_i$ minutes — otherwise, you lose to that opponent.

You have $m$ minutes in total to prepare for matches, but you can prepare for only one match at one moment. In other words, if you want to win against opponents $p_1, p_2, \dots, p_k$, you need to spend $a_{p_1} + a_{p_2} + \dots + a_{p_k}$ minutes for preparation — and if this number is greater than $m$, you cannot achieve a win against all of these opponents at the same time.

The final place of each contestant is equal to the number of contestants with strictly more wins $+$ $1$. For example, if $3$ contestants have $5$ wins each, $1$ contestant has $3$ wins and $2$ contestants have $1$ win each, then the first $3$ participants will get the $1$-st place, the fourth one gets the $4$-th place and two last ones get the $5$-th place.

Calculate the minimum possible place (lower is better) you can achieve if you can't prepare for the matches more than $m$ minutes in total.

你正在参加“又一场比赛”（Yet Another Tournament）。共有 $n + 1$ 名参赛者：你和其余 $n$ 名对手，编号从 $1$ 到 $n$。

每两名参赛者之间恰好进行一场比赛。当对手 $i$ 与对手 $j$ 比赛时，当且仅当 $i > j$ 时，对手 $i$ 获胜。

当你与对手 $i$ 比赛时，情况变得稍微复杂一些。为了战胜对手 $i$，你必须至少为此场比赛准备 $a_i$ 分钟；否则，你将输给该对手。

你总共只有 $m$ 分钟可用于赛前准备，且同一时刻只能为一场比赛做准备。换言之，若你想战胜对手 $p_1, p_2, \dots, p_k$，则需花费 $a_{p_1} + a_{p_2} + \dots + a_{p_k}$ 分钟进行准备；若该总和超过 $m$，则你无法同时战胜所有这些对手。

每位参赛者的最终名次等于“严格胜场数比他多的参赛者人数”加 $1$。例如，若有 $3$ 名参赛者各胜 $5$ 场，$1$ 名参赛者胜 $3$ 场，另有 $2$ 名参赛者各胜 $1$ 场，则前 $3$ 名参赛者获得第 $1$ 名，第 $4$ 名参赛者获得第 $4$ 名，最后 $2$ 名参赛者均获得第 $5$ 名。

在总计准备时间不超过 $m$ 分钟的前提下，求你能取得的最小可能名次（数值越小越好）。

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains two integers $n$ and $m$ ($1 \le n \le 5 \cdot 10^5$; $0 \le m \le \sum\limits_{i=1}^{n}{a_i}$) — the number of your opponents and the total time you have for preparation.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 1000$), where $a_i$ is the time you need to prepare in order to win against the $i$-th opponent.

It's guaranteed that the total sum of $n$ over all test cases doesn't exceed $5 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$1 \le n \le 5 \cdot 10^5$；$0 \le m \le \sum\limits_{i=1}^{n}{a_i}$）—— 你的对手数量以及你用于准备的总时间。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \le a_i \le 1000$），其中 $a_i$ 表示你为战胜第 $i$ 个对手所需花费的准备时间。

保证所有测试用例中 $n$ 的总和不超过 $5 \cdot 10^5$。

For each test case, print the minimum possible place you can take if you can prepare for the matches no more than $m$ minutes in total.

对于每个测试用例，输出在总共最多准备 $m$ 分钟的情况下，你能获得的最小可能名次。

In the first test case, you can prepare to all opponents, so you'll win $4$ games and get the $1$-st place, since all your opponents win no more than $3$ games.

In the second test case, you can prepare against the second opponent and win. As a result, you'll have $1$ win, opponent $1$ — $1$ win, opponent $2$ — $1$ win, opponent $3$ — $3$ wins. So, opponent $3$ will take the $1$-st place, and all other participants, including you, get the $2$-nd place.

In the third test case, you have no time to prepare at all, so you'll lose all games. Since each opponent has at least $1$ win, you'll take the last place (place $6$).

In the fourth test case, you have no time to prepare, but you can still win against the first opponent. As a result, opponent $1$ has no wins, you have $1$ win and all others have at least $2$ wins. So your place is $4$.

在第一个测试用例中，你可以为所有对手做准备，因此你将赢得 $4$ 场比赛并获得第 $1$ 名，因为你的所有对手最多只赢得 $3$ 场比赛。

在第二个测试用例中，你可以为第二位对手做准备并获胜。结果是：你有 $1$ 场胜利，对手 $1$ 有 $1$ 场胜利，对手 $2$ 有 $1$ 场胜利，对手 $3$ 有 $3$ 场胜利。因此，对手 $3$ 将获得第 $1$ 名，其余所有参赛者（包括你）均获得第 $2$ 名。

在第三个测试用例中，你完全没时间做准备，因此你将输掉所有比赛。由于每位对手至少有 $1$ 场胜利，你将获得最后一名（即第 $6$ 名）。

在第四个测试用例中，你没有时间做准备，但仍可战胜第一位对手。结果是：对手 $1$ 没有胜场，你有 $1$ 场胜利，而其他所有对手至少有 $2$ 场胜利。因此，你的名次为第 $4$ 名。