#2050 Normal Distribution

2 s   128 MB  

Description

 

Hyun-hwan is the instructor for ACM-ICPC contestants in Ajou University. Last week, he held a team selection contest for the seoul regional contest. After the contest is over, he calculated scores of each contestants using an obscure formula. According to this formula, each contest receives a score between 0 to N-1(inclusive) and N is multiple of 10.

As a measure of the quality of the problem set, we want to find out if distribution of the scores follow the normal distribution or not: we believe a better problem set will result in normally distributed scores. Unfortunately, Hyun-hwan is not good at statistics, so he came up with a simple alternative procedure. The procedure is as follows:

Let f[i]=(number of scores between 10i to 10i+9) ( 0 ≤ i ≤ N/10-i ) Then, if the following relation:

f[0] < f[1] < ... < f[k] > f[k + 1] > ... > f[N/10 − 1]

holds for some k ( k > 0 and N/10-1-k > 0 ), we can say 'the distribution of the scores is similar to normal distribution', otherwise, we can’t say that.

Write a program that will determine distribution of given scores is similar to normal distribution.

Input

Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. In the first line of each case, two integers S (1 ≤ S ≤ 20,000 ) and N ( 10 ≤ N ≤ 100 ) will be given. In the second line of each case, scores of S contestants will be given.

Output

Your program is to write to standard output. Print exactly one line for each test case. For each test case, print ‘YES’ if the distribution of the scores is similar to normal distribution, otherwise print ‘NO’(without quotes).

Sample Input

Sample Output

2
6 30
5 9 10 18 19 21
4 20
0 0 19 19
YES
NO