Yet another MEX problem Solution
The MEX (minimum excluded) of an array is the smallest non-negative integer that does not belong to the array. For instance:
- The MEX of [2,2,1] is 0, because 0 does not belong to the array.
- The MEX of [3,1,0,1] is 2, because 0 and 1 belong to the array, but 2 does not.
- The MEX of [0,3,1,2] is 4, because 0,1,2 and 3 belong to the array, but 4 does not.
You are given an array A of length N. You create a list B consisting of the MEX-es of all subarrays of the array A. Formally, for all pairs (l,r) such that 1≤l≤r≤N, you calculate MEX(Al,Al+1,…,Ar) and append the value in the list B. Find the K-th smallest value in the list B.
Note: Since the size of the input and output is large, please use fast input-output methods.
- The first line contains T denoting the number of test cases. Then the test cases follow.
- The first line of each test case contains two space-separated integers N and K.
- The second line contains N space-separated integers A1,A2,…,AN denoting the given array.
For each test case, output on a single line the K-th smallest value in the list B.
- Sum of N over all test cases does not exceed 2⋅106.
Subtask 1 (10 points):
- Sum of NN over all test cases does not exceed 5⋅104.
Subtask 2 (90 points): Original constraints
Sample Input 1
3 3 4 1 0 2 3 2 2 1 3 3 6 0 1 2
Sample Output 1
1 0 3
Test case 1: MEX(A1)=0, MEX(A1,A2)=2, MEX(A1,A2,A3)=3, MEX(A2)=1, MEX(A2,A3)=1, MEX(A3)=0. Hence the list B=[0,2,3,1,1,0] and the 4-th smallest value in B is 1.
Test case 2: The MEX of all subarrays of the array A is 0. Hence the 2-nd smallest element in the list B is 0.