You are given a sorted array of integers (a_1, a_2, \dots, a_n). We can perform any number of operations of the following type on this array: mark the first element of the array, as well as all elements that are not equal to their left neighbors (that is, all elements (i) such that (a_i \ne a_{i-1})). then either delete all marked elements or duplicate them (that is, replace each marked element with two identical elements). For example, consider the array (\mathbf{1}, 1, 1, \mathbf{2}, \mathbf{4}, 4, \mathbf{5}) (marked elements are shown in bold). If we delete all marked elements, we get (1, 1, 4), and if we duplicate them, we get (1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5). The operations cannot be performed if the array becomes empty. After each operation, every element gets unmarked. We call an array of integers (b) reachable if it can be obtained from array (a) by some number of the described operations. Your task is to count the number of reachable arrays of length (k). The first line contains one integer (t) ((1 \le t \le 10^4)) — the number of test cases. Each test case consists of two lines: the first line contains two integers (n) and (k) ((1 \le n, k \le 3 \cdot 10^5)); the second line contains (n) integers (a_1, a_2, \dots, a_n) ((1 \le a_1 \le a_2 \le \dots \le a_n \le n)). Note that the array is sorted. Additional constraint on the input: the sum of (n) over all test cases does not exceed (3 \cdot 10^5). For each test case, output one integer — the number of reachable arrays (b) of length (k). It can be shown that, under the constraints of the problem, the answer fits into a standard (32)-bit integer type. In the first example, the following sequence of operations can be performed: (\mathbf{1} \rightarrow \mathbf{1}, 1 \rightarrow \mathbf{1}, 1, 1 \rightarrow \mathbf{1}, 1, 1, 1 \rightarrow 1, 1, 1, 1, 1). In the second example, it is impossibl