B'You are given an array b_1, b_2, ldots, b_n . An anonymous informant has told you that the array b was obtained as follows: initially, there existed an array a_1, a_2, ldots, a_n , after which the following two-component operation was performed k times: As a result of k such operations, the array b_1, b_2, ldots, b_n was obtained. You want to check if the words of the anonymous informant can be true or if they are guaranteed to be false. ^{ dagger} A number x is called a fixed point of the array a_1, a_2, ldots, a_n if 1 <= q x <= q n and a_x = x . ^{ ddagger} A cyclic left shift of the array a_1, a_2, ldots, a_n is the array a_2, ldots, a_n, a_1 . Each test contains multiple test cases. The first line contains an integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The description of the test cases follows. The first line of each test case contains two integers n, k ( 1 <= n <= 2 cdot 10^5 , 1 <= k <= 10^9 ) -- the length of the array b and the number of operations performed. The second line of each test case contains n integers b_1, b_2, ldots, b_n ( 1 <= b_i <= 10^9 ) -- the elements of the array b . It is guaranteed that the sum of the values of n for all test cases does not exceed 2 cdot 10^5 . For each test case, output "Yes" if the words of the anonymous informant can be true, and "No" if they are guaranteed to be false. In the first test case, the array a could be equal to [3, 2, 3, 4, 3] . In the first operation, a fixed point x = 2 was chosen, and after 2 left shifts, the array became [3, 4, 3, 3, 2] . In the second operation, a fixed point x = 3 was chosen, and after 3 left shifts, the array became [3, 2, 3, 4, 3] . In the third operation, a fixed point x = 3 was chosen again, and after 3 left shifts, the array became [4'...