Baltic, a famous chess player who is also a mathematician, has an array $$$a_1,a_2, \ldots, a_n$$$, and he can perform the following operation several (possibly $$$0$$$) times:
Baltic's favorite number is $$$m$$$, and he wants $$$a_1 + a_2 + \cdots + a_m$$$ to be the smallest of all non-empty prefix sums. More formally, for each $$$k = 1,2,\ldots, n$$$ it should hold that $$$$$$a_1 + a_2 + \cdots + a_k \geq a_1 + a_2 + \cdots + a_m.$$$$$$
Please note that multiple smallest prefix sums may exist and that it is only required that $$$a_1 + a_2 + \cdots + a_m$$$ is one of them.
Help Baltic find the minimum number of operations required to make $$$a_1 + a_2 + \cdots + a_m$$$ the least of all prefix sums. It can be shown that a valid sequence of operations always exists.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \leq t \leq 10\,000$$$). The description of the test cases follows.
The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq m \leq n \leq 2\cdot 10^5$$$) — the size of Baltic's array and his favorite number.
The second line contains $$$n$$$ integers $$$a_1,a_2, \ldots, a_n$$$ ($$$-10^9 \leq a_i \leq 10^9$$$) — the array.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.
For each test case, print a single integer — the minimum number of required operations.
64 3-1 -2 -3 -44 31 2 3 41 115 5-2 3 -5 1 -205 2-2 3 -5 -5 -2010 4345875723 -48 384678321 -375635768 -35867853 -35863586 -358683842 -81725678 38576 -357865873
1 1 0 0 3 4
In the first example, we perform the operation $$$a_4 := -a_4$$$. The array becomes $$$[-1,-2,-3,4]$$$ and the prefix sums, $$$[a_1, \ a_1+a_2, \ a_1+a_2+a_3, \ a_1+a_2+a_3+a_4]$$$, are equal to $$$[-1,-3,-6,-2]$$$. Thus $$$a_1 + a_2 + a_3=-6$$$ is the smallest of all prefix sums.
In the second example, we perform the operation $$$a_3 := -a_3$$$. The array becomes $$$[1,2,-3,4]$$$ with prefix sums equal to $$$[1,3,0,4]$$$.
In the third and fourth examples, $$$a_1 + a_2 + \cdots + a_m$$$ is already the smallest of the prefix sums — no operation needs to be performed.
In the fifth example, a valid sequence of operations is:
The array becomes $$$[-2,-3,5,-5,20]$$$ and its prefix sums are $$$[-2,-5,0,-5,15]$$$. Note that $$$a_1+a_2=-5$$$ and $$$a_1+a_2+a_3+a_4=-5$$$ are both the smallest of the prefix sums (and this is a valid solution).