Anonymous Informant Solution Codeforces

Anonymous Informant Solution Codeforces

time limit per test

3 seconds

memory limit per test

512 megabytes

input

standard input

output

standard output

You are given an array b1,b2,,bn�1,�2,…,��.

An anonymous informant has told you that the array b was obtained as follows: initially, there existed an array a1,a2,,an�1,�2,…,��, after which the following two-component operation was performed k times:

  1. A fixed point x of the array a was chosen.
  2. Then, the array a was cyclically shifted to the left exactly x times.

As a result of k such operations, the array b1,b2,,bn�1,�2,…,�� was obtained. You want to check if the words of the anonymous informant can be true or if they are guaranteed to be false.

A number x is called a fixed point of the array a1,a2,,an�1,�2,…,�� if 1xn1≤�≤� and ax=x��=�.

A cyclic left shift of the array a1,a2,,an�1,�2,…,�� is the array a2,,an,a1�2,…,��,�1.

Input

Each test contains multiple test cases. The first line contains an integer t (1t1041≤�≤104) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers n,k�,� (1n21051≤�≤2⋅1051k1091≤�≤109) — the length of the array b and the number of operations performed.

The second line of each test case contains n integers b1,b2,,bn�1,�2,…,�� (1bi1091≤��≤109) — the elements of the array b.

It is guaranteed that the sum of the values of n for all test cases does not exceed 21052⋅105.

Output

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.

Example
input

Copy
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
output

Copy
Yes
Yes
No
Yes
Yes
No
Note

In the first test case, the array a could be equal to [3,2,3,4,3][3,2,3,4,3]. In the first operation, a fixed point x=2�=2 was chosen, and after 22 left shifts, the array became [3,4,3,3,2][3,4,3,3,2]. In the second operation, a fixed point x=3�=3 was chosen, and after 33 left shifts, the array became [3,2,3,4,3][3,2,3,4,3]. In the third operation, a fixed point x=3�=3 was chosen again, and after 33 left shifts, the array became [4,3,3,2,3][4,3,3,2,3], which is equal to the array b.

In the second test case, the array a could be equal to [7,2,1][7,2,1]. After the operation with a fixed point x=2�=2, the array became [1,7,2][1,7,2]. Then, after the operation with a fixed point x=1�=1, the array returned to its initial state [7,2,1][7,2,1]. These same 22 operations (with x=2�=2, and x=1�=1) were repeated 4949 times. So, after 100100 operations, the array returned to [7,2,1][7,2,1].

In the third test case, it can be shown that there is no solution.

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