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 ($$$j \gt i$$$).

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.

Money Buys Less Happiness Now

Examples