CF 1759B - Lost Permutation

A sequence of n numbers is called a permutation if it contains all integers from 1 to n exactly once.

For example, the sequences [3,1,4,2], [1] and [2,1] are Permutations, but [1,2,1], [0,1] and [1,3,4] — are not.

Polycarp lost his favorite permutation and found only some of its elements — the numbers b1,b2,…bm.

He is sure that the sum of the lost elements equals s.

Determine whether one or more numbers can be appended to the given sequence b1,b2,…bm

 such that the sum of the added numbers equals s, and the resulting new array is a permutation?

Input

The first line of input contains a single integer t (1≤t≤100) —the number of test cases.

Then the descriptions of the test cases follow.

The first line of each test set contains two integers m and s (1≤m≤50, 1≤s≤1000)

—-the number of found elements and the sum of forgotten numbers.

The second line of each test set contains m different integers b1,b2…bm (1≤bi≤50)

 — the elements Polycarp managed to find.

Output

Print t lines, each of which is the answer to the corresponding test set.

 Print as the answer YES if you can append several elements to the array b,

  that their sum equals s and the result will be a permutation. Output NO otherwise.

You can output the answer in any case (for example, yEs, yes, Yes and YES will be recognized as positive answer).

Example

input

5

3 13

3 1 4

1 1

1

3 3

1 4 2

2 1

4 3

5 6

1 2 3 4 5

output

YES

NO

YES

NO

YES

Note

In the test case of the example, m=3,s=13,b=[3,1,4].

You can append to b the numbers 6,2,5, the sum of which is 6+2+5=13.

 Note that the final array will become [3,1,4,6,2,5], which is a permutation.

In the second test case of the example, m=1,s=1,b=[1]. You cannot append one or more numbers to [1]

 such that their sum equals 1 and the result is a permutation.

In the third test case of the example, m=3,s=3,b=[1,4,2]. You can append the number 3 to b.

 Note that the resulting array will be [1,4,2,3], which is a permutation.

-------------------------------------------------

用循环去处理，一个是从1递增的一个变量，如果在数组中，那么数组减去这个值，变量加1，数组往后移动一位，如果不在数组中，则s值减去这个值，依次循环到数组结束，

如果此时s还大于0，继续-i，然后i++，如果最后s正好等于零，那么说明是可以的，不等于零，就不可以，输出即可。