A16342 · Anonymous Informant

题目描述

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: 1. A fixed point $^{\dagger}$ $x$ of the array $a$ was chosen. 2. Then, the array $a$ was cyclically shifted to the left $^{\ddagger}$ exactly $x$ 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 $1 \leq x \leq n$ 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 $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of the test cases follows. The first line of each test case contains two integers $n, k$ ( $1 \le n \le 2 \cdot 10^5$ , $1 \le k \le 10^9$ ) — the length of the array $b$ and the number of operations performed. The second line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \le b_i \le 10^9$ ) — 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.

输入 #1

6
5 3
4 3 3 2 3
3 100
7 2 1
5 5
6 1 1 1 1
1 1000000000
1
8 48
9 10 11 12 13 14 15 8
2 1
1 42

输出 #1

Yes
Yes
No
Yes
Yes
No