A15521 | 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 $b_1, b_2, \dots b_m$ . 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 $b_1, b_2, \dots b_m$ such that the sum of the added numbers equals $s$ , and the resulting new array is a permutation?

The first line of input contains a single integer $t$ ( $1 \le t \le 100$ ) —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 $s$ ( $1 \le m \le 50$ , $1 \le s \le 1000$ )—-the number of found elements and the sum of forgotten numbers.

The second line of each test set contains $m$ different integers $b_1, b_2 \dots b_m$ ( $1 \le b_i \le 50$ ) — the elements Polycarp managed to find.

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).