| [Shirobon - FOX](https://soundcloud.com/shirobon/fox?in=mart_207/sets/fav) | |
| ⠀ | |
| You are given $n$ points on the $x$ axis, at increasing positive integer coordinates $x_1 < x_2 < \ldots < x_n$. | |
| For each pair $(i, j)$ with $1 \leq i < j \leq n$, you draw the segment $[x_i, x_j]$. The segments are closed, i.e., a segment $[a, b]$ contains the points $a, a+1, \ldots, b$. | |
| You are given $q$ queries. In the $i$-th query, you are given a positive integer $k_i$, and you have to determine how many points with integer coordinates are contained in exactly $k_i$ segments. | |
| Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows. | |
| The first line of each test case contains two integers $n$, $q$ ($2 \le n \le 10^5$, $1 \le q \le 10^5$) — the number of points and the number of queries. | |
| The second line of each test case contains $n$ integers $x_1, x_2, \ldots, x_n$ ($1 \leq x_1 < x_2 < \ldots < x_n \leq 10^9$) — the coordinates of the $n$ points. | |
| The third line of each test case contains $q$ integers $k_1, k_2, \ldots, k_q$ ($1 \leq k_i \leq 10^{18}$) — the parameters of the $q$ queries. | |
| It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$, and the sum of $q$ over all test cases does not exceed $10^5$. | |
| For each test case, output a single line with $q$ integers: the $i$-th integer is the answer to the $i$-th query. | |
| In the first example, you only draw the segment $[101, 200]$. No point is contained in exactly $2$ segments, and the $100$ points $101, 102, \ldots, 200$ are contained in exactly $1$ segment. | |
| In the second example, you draw $15$ segments: $[1, 2], [1, 3], [1, 5], [1, 6], [1, 7], [2, 3], [2, 5], [2, 6], [2, 7], [3, 5], [3, 6], [3, 7], [5, 6], [5, 7], [6, 7]$. Points $1, 7$ are contained in exactly $5$ segments; points $2, 4, 6$ are contained in exactly $9$ segments; points $3, 5$ are contained in exactly $11$ segments. |