Problem:
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, i-th of which denotes number of participants solving the i-th 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 ≤ 108
  • 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.

Solution:

#include <iostream>
using namespace std;
int main() {
    int t;
    cin>>t;
    while(t--)
    {
        int n, p,temp;
        cin>>n>>p;
        int cake=0,hard=0;
        while(n--)
        {
            cin>>temp;
            if(temp >= p/2) cake++;
            else if(temp<= p/10) hard++;
        }
        
        if(hard==2 and cake==1)
        cout<<"yes"<<endl;
        else cout<<"no"<<endl;
    
    }
    return 0;
}