Yet Again a Subarray Problem

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### Read problem statements in [Hindi](http://www.codechef.com/download/translated/MAR19TST/hindi/SUBPRNJL.pdf), [Bengali](http://www.codechef.com/download/translated/MAR19TST/bengali/SUBPRNJL.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/MAR19TST/mandarin/SUBPRNJL.pdf), [Russian](http://www.codechef.com/download/translated/MAR19TST/russian/SUBPRNJL.pdf), and [Vietnamese](http://www.codechef.com/download/translated/MAR19TST/vietnamese/SUBPRNJL...) as well. "It does not matter how slowly you go as long as you do not stop."  Confucius You are given an array $A_1, A_2, \ldots, A_N$ and an integer $K$. For each subarray $S = [A_l, A_{l+1}, \ldots, A_r]$ ($1 \le l \le r \le N$):  Let's define an array $B$ as $S$ concatenated with itself $m$ times, where $m$ is the smallest integer such that $m(rl+1) \ge K$.  Next, let's sort $B$ and define $X = B_K$, i.e. as a $K$th smallest element of $B$. Note that $B \ge K$.  Then, let's define $F$ as the number of occurrences of $X$ in $S$.  The subarray $S$ is *beautiful* if $F$ occurs in $S$ at least once. Find the number of beautiful subarrays of $A$. Two subarrays $A_l, A_{l+1}, \ldots, A_r$ and $A_p, A_{p+1}, \ldots, A_q$ are different if $l \neq p$ or $r \neq q$. ### Input  The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.  The first line of each test case contains two spaceseparated integers $N$ and $K$.  The second line contains $N$ spaceseparated integers $A_1, A_2, \ldots, A_N$. ### Output For each test case, print a single line containing one integer  the number of beautiful subarrays. ### Constraints  $1 \le T \le 5$  $1 \le N \le 2,000$  $1 \le K \le 10^9$  $1 \le A_i \le 2000$ for each valid $i$ ### Subtasks **Subtask #1 (20 points):** $1 \le N \le 200$ **Subtask #2 (80 points):** original constraints ### Example Input ``` 1 3 3 1 2 3 ``` ### Example Output ``` 3 ``` ### Explanation **Example case 1:** There are six subarrays of $A$: $[1]$, $[2]$, $[3]$, $[1, 2]$, $[2, 3]$, $[1, 2, 3]$. The corresponding arrays $B$ are $[1, 1, 1]$, $[2, 2, 2]$, $[3, 3, 3]$, $[1, 2, 1, 2]$, $[2, 3, 2, 3]$, $[1, 2, 3]$. Three of the subarrays are beautiful: $[1]$, $[1, 2]$ and $[1, 2, 3]$. For these subarrays, $X$ is $1$, $2$ and $3$ respectively (for example, for $S = [1, 2]$, $B = [1, 2, 1, 2]$ is sorted to $[1, 1, 2, 2]$ and $X = 2$ is the $3$rd element). Then, $F = 1$ for each of these subarrays, and each of these subarrays contains $1$.Author:  prnjl_rai 
Editorial  https://discuss.codechef.com/problems/SUBPRNJL 
Tags  binarysearch, easy, march19, partialsums, prnjl_rai, segmenttree, taran_1407 
Date Added:  23022019 
Time Limit:  2 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS 
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