#P1974G. Money Buys Less Happiness Now
Money Buys Less Happiness Now
Description
You can never buy enough happiness, so here we go again! In this version, you can only buy $h_i = 1$ unit of happiness each month, but the number of months is hugely increased. We are in the realm of quantum happiness and time dilation.
Being a physicist, Charlie likes to plan his life in simple and precise terms.
For the next $m$ months, starting with no money, Charlie will work hard and earn $x$ pounds per month. For the $i$-th month $(1 \le i \le m)$, there'll be a single opportunity of paying cost $c_i$ pounds to obtain one unit of happiness. You cannot buy more than one unit each month.
Borrowing is not allowed. Money earned in the $i$-th month can only be spent in a later $j$-th month ($j>i$).
Since physicists don't code, help Charlie find the maximum reachable units of happiness.
The first line of the input contains $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains two integers, $m$ and $x$ ($1 \le m \le 2 \cdot 10^5$, $1 \le x \le 10^3$) — the total number of months and the monthly salary.
The second line of each test case contains $m$ integers $c_1, c_2, \dots, c_m$ ($1 \leq c_i \leq 10^3$) — the cost of one unit of happiness for each month.
It is guaranteed that sum of $m$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case, output one integer — the maximal amount of happiness Charlie can get.
Input
The first line of the input contains $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains two integers, $m$ and $x$ ($1 \le m \le 2 \cdot 10^5$, $1 \le x \le 10^3$) — the total number of months and the monthly salary.
The second line of each test case contains $m$ integers $c_1, c_2, \dots, c_m$ ($1 \leq c_i \leq 10^3$) — the cost of one unit of happiness for each month.
It is guaranteed that sum of $m$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, output one integer — the maximal amount of happiness Charlie can get.
6
3 3
2 2 2
6 5
2 2 8 2 6 8
6 4
4 10 3 8 6 10
2 1
1 1
4 1
4 1 3 1
4 2
1 3 4 3
2
4
3
1
2
1