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Let's Be an Anagrammatist

Limits: 1s, 512 MB

Do you know what is an anagram? An anagram is a rearrangement of letters of one word to form another word. For example: one of the anagrams of the word “CODEMASK” can be “DEMOCSAK”. So, we can find different kinds of anagram of a word.

Now, you are given two array S & T. You have to find a lexicographically smallest contiguous subsequence of S which is an anagram of array T.

Between two sequence A & B, where length(A) == length(B), A will be lexicographically smaller than B if we can find an index i (1 <= i <= length(A)) where A[i] < B[i] and for all j, A[j] = B[j] where 1 <= j < i.

Input

The first line of the input is the number of the test cases Ts (1 <= Ts <= 20).

Each test case contains three lines. The first lines contains N & M (1 <= N, M <= 200000), N is the length of array S & M is the length of array T (1 <= S[i], T[i] <= 200000).

Next line contains N integers of array S. Then another lines follows contains M integers describing array T.

Output

First you need to print the case number. Then on the same line, you have to print the index (1 based) of the lexicographically smallest contiguous subsequence of S which is an anagram of T. If there is more than one answer, you need to print the smallest index. If you can’t find any anagram of the T in S, just print 0.

Samples

InputOutput
2
4 3
1 3 2 4
1 2 3
5 3
3 2 1 4 10
1 2 4
Case 1: 1
Case 2: 2

This problem was authored for CodeMask Championship 2016 and is being hosted on Toph per organizer’s request.

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