P16755 [GKS 2020 #C] Countdown

Avery has an array of $N$ positive integers. The i-th integer of the array is $A_i$. A contiguous subarray is an $m$-countdown if it is of length $m$ and contains the integers $m, m-1$, $m-2, ..., 2, 1$ in that order. For example, $[3, \;\; 2, \;\; 1]$ is a $3$-countdown. Can you help Avery count the number of $K$-countdowns in her array?

The first line of the input gives the number of test cases, $T$. $T$ test cases follow. Each test case begins with a line containing the integers $N$ and $K$. The second line contains $N$ integers. The i-th integer is $A_i$.

For each test case, output one line containing Case #x: y, where $x$ is the test case number (starting from $1$) and $y$ is the number of $K$-countdowns in her array.

In sample case #1, there are two 3-countdowns as highlighted below. - 1 2 3 7 9 **3 2 1** 8 3 2 1 - 1 2 3 7 9 3 2 1 8 **3 2 1** In sample case #2, there are no 2-countdowns. In sample case #3, there is one 6-countdown as highlighted below. - 100 7 **6 5 4 3 2 1** 100 ### Limits $1 \le T \le 100$. $2 \le K \le N$. $1 \le A_i \le 2 \times 10^5$, for all $i$. **Test Set 1** $2 \le N \le 1000$. **Test Set 2** $2 \le N \le 2 \times 10^5$ for at most $10$ test cases. For the remaining cases, $2 \le N \le 1000$.