Alice has N students in his class, numbered 1 through N. The ith student has expertise in a subject numbered Ai.
Alice has to divide the students into two teams. The uniqueness of a team is defined as the number of distinct subjects such that there is atleast one student in the team with expertise in the subject. For example, the uniqueness of a team denoted by A=[1,3,1,4,4] is 3.
Alice wants to distribute the students of the class into two teams such that each student belongs to exactly one team and the uniqueness of each team is exactly K. Will he be able to do so?
Input format
Output format
For each test case, print YES if Alice is able to make two teams satisfying the given conditions, otherwise print NO.
Constraints
1≤T≤1052≤N≤1051≤K≤N1≤Ai≤NSum of N over all test cases does not exceed 3⋅105.