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 10*i to 10*i+9 ( 0 <= i <= N/10-1 ) Then, if the following relation
f < f < ... < 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.
Your program is to read from standard input. The input consists of T test cases. The number of test cases T (1 <= T <= 20) 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.
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 ‘
2 6 30 5 9 10 18 19 21 4 20 0 0 19 19