# 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

• Subtask #1 (40 points): P is a multiple of 10
• Subtask #2 (60 points): Original constraints

```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.`