CodeChef : October Challenge 2017 – A Balanced Contest

By | October 7, 2017

A Balanced Contest

Source: CodeChef

A Balanced Contest : 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 Nproblems 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

Its a simple question. Just need to check conditions.