B. Lost Permutationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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?InputThe 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.OutputPrint 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).ExampleInput
53 133 1 41 113 31 4 22 14 35 61 2 3 4 5Output
YES
NO
YES
NO
YES
NoteIn 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.
53 133 1 41 113 31 4 22 14 35 61 2 3 4 5
YES NO YES NO YES 
['math', '*800']