G. Money Buys Less Happiness Now
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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.

Example
Input
63 32 2 26 52 2 8 2 6 86 44 10 3 8 6 102 11 14 14 1 3 14 21 3 4 3
Output
2
4
3
1
2
1