A Balanced Contest

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Chef wants to organize a contest. Predicting difficulty levels of the problems can be a daunting task. Chef wants his contests to be balanced in terms of difficulty levels of the problems.
Assume a contest had total P participants. A problem that was solved by at least half of the participants (i.e. P / 2 (integer division)) is said to be cakewalk difficulty. A problem solved by at max P / 10 (integer division) participants is categorized to be a hard difficulty.
Chef wants the contest to be balanced. According to him, a balanced contest must have exactly 1 cakewalk and exactly 2 hard problems. You are given the description of N problems and the number of participants solving those problems. Can you tell whether the contest was balanced or not?
Input
The first line of the input contains an integer T denoting the number of test cases.
The first line of each test case contains two space separated integers, N, P denoting the number of problems, number of participants respectively.
The second line contains N space separated integers, ith of which denotes number of participants solving the ith problem.
Output
For each test case, output "yes" or "no" (without quotes) denoting whether the contest is balanced or not.
Constraints
 1 ≤ T, N ≤ 500
 1 ≤ P ≤ 10^{8}
 1 ≤ Number of participants solving a problem ≤ P
Subtasks
 Subtask #1 (40 points): P is a multiple of 10
 Subtask #2 (60 points): Original constraints
Example
Input 6 3 100 10 1 100 3 100 11 1 100 3 100 10 1 10 3 100 10 1 50 4 100 50 50 50 50 4 100 1 1 1 1 Output yes no no yes no no
Explanation
Example case 1.: The problems are of hard, hard and cakewalk difficulty. There is 1 cakewalk and 2 hard problems, so the contest is balanced.
Example case 2.: The second problem is hard and the third is cakewalk. There is 1 cakewalk and 1 hard problem, so the contest is not balanced.
Example case 3.: All the three problems are hard. So the contest is not balanced.
Example case 4.: The problems are of hard, hard, cakewalk difficulty. The contest is balanced.
Example case 5.: All the problems are cakewalk. The contest is not balanced.
Example case 6.: All the problems are hard. The contest is not balanced.
Author:  admin2 
Tester:  alex_2oo8 
Editorial  https://discuss.codechef.com/problems/PERFCONT 
Tags  admin2, cakewalk, oct17 
Date Added:  9092017 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, CLOJ, COB, FS 
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