#### A Balanced Contest

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 **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**≤ 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

Input6 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 1Outputyes 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.