Two integer arrays (a) and (b) of size (n) are complementary if there exists an integer (x) such that (a_i + b_i = x) over all (1 \le i \le n). For example, the arrays (a = 2, 1, 4) and (b = 3, 4, 1) are complementary, since (a_i + b_i = 5) over all (1 \le i \le 3). However, the arrays (a = 1, 3) and (b = 2, 1) are not complementary. Cow the Nerd thinks everybody is interested in math, so he gave Cherry Bomb two integer arrays (a) and (b). It is known that (a) and (b) both contain (n) non-negative integers not greater than (k). Unfortunately, Cherry Bomb has lost some elements in (b). Lost elements in (b) are denoted with (-1). Help Cherry Bomb count the number of possible arrays (b) such that: (a) and (b) are complementary . All lost elements are replaced with non-negative integers no more than (k). The first line of the input contains a single integer (t) ((1 \le t \le 10^4)) — the number of test cases. The first line of each test case contains two integers (n) and (k) ((1 \le n \le 2 \cdot 10^5), (0 \le k \le 10^9)) — the size of the arrays and the maximum possible value of their elements. The second line contains (n) integers (a_1, a_2, ..., a_n) ((0 \le a_i \le k)). The third line contains (n) integers (b_1, b_2, ..., b_n) ((-1 \le b_i \le k)). If (b_i = -1), then this element is missing. It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). Output exactly one integer, the number of ways Cherry Bomb can fill in the missing elements from (b) such that (a) and (b) are complementary. In the first example, the only way to fill in the missing elements in (b) such that (a) and (b) are complementary is if (b = 2, 0, 1). In the second example, there is no way to fill in the missing elements of (b) such that (a) and (b)