Problem:
Score : 700 points

Problem Statement

Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).

Now, he will perform the following operation exactly once:

Choose K consecutive elements in P and sort them in ascending order.

Find the number of permutations that can be produced as P after the operation.

Constraints

2 \leq N \leq 200000

2 \leq K \leq N

0 \leq P_i \leq N-1

P_0,P_1,\cdots,P_{N-1} are all different.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_0 P_1 \cdots P_{N-1}

Output

Print the number of permutations that can be produced as P after the operation.

Sample Input 1

5 3
0 2 1 4 3

Sample Output 1

2

Two permutations can be produced as P after the operation: (0,1,2,4,3) and (0,2,1,3,4).

Sample Input 2

4 4
0 1 2 3

Sample Output 2

1

Sample Input 3

10 4
2 0 1 3 7 5 4 6 8 9

Sample Output 3

6

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.*

fun main(args: Array<String>) = IO().exec {
    val n = int()
    val k = int()
    val p = IntArray(n){int()}
    val tset = TreeSet<Int>()
    var initState = false
    for (i in k) tset.add(p[i])
    var cnt = 0
    for (i in k-1) if (p[i] < p[i+1]) cnt++ else cnt=0
    if (cnt >= k-1) initState=true
    var ret = 1
    for (i in k until n) {
        if (p[i-1] < p[i]) cnt++ else cnt=0
        if (!(p[i] > tset.last() && p[i-k] == tset.first())) {
            if (cnt >= k-1) initState=true else ret++
        }
        tset.remove(p[i-k])
        tset.add(p[i])
    }
    println(ret + if (initState) 1 else 0)
}

// region template
operator fun Int.iterator() = 0.until(this).iterator()

class IO {
    val printable = 33..126
    val buffer = ByteArray(1024)
    var ptr = 0
    var buflen = 0
    val out = java.io.PrintWriter(System.out)
    fun hasNextByte(): Boolean = if (ptr < buflen) true else {
        ptr = 0
        buflen = System.`in`.read(buffer)
        buflen > 0
    }

    fun readByte(): Byte = if (hasNextByte()) buffer[ptr++] else -1
    fun hasNext(): Boolean {
        while (hasNextByte() && buffer[ptr] !in printable) ptr++
        return hasNextByte()
    }

    fun string(): String {
        if (!hasNext()) throw java.util.NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (b in printable) {
            sb.appendCodePoint(b.toInt())
            b = readByte()
        }
        return sb.toString()
    }

    fun long(): Long {
        if (!hasNext()) throw java.util.NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if (b == '-'.toByte()) {
            minus = true
            b = readByte()
        }
        if (b !in '0'.toByte()..'9'.toByte()) {
            throw NumberFormatException()
        }
        while (true) {
            if (b in '0'.toByte()..'9'.toByte()) {
                n *= 10
                n += b - '0'.toByte()
            } else if (b == (-1).toByte() || b !in printable) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun int(): Int {
        val nl = long()
        if (nl !in Integer.MIN_VALUE..Integer.MAX_VALUE) throw NumberFormatException()
        return nl.toInt()
    }

    fun double(): Double = string().toDouble()
    fun print(obj: Any) = out.print(obj)
    fun print(i: Int) = out.print(i)
    fun print(l: Long) = out.print(l)
    fun println(obj: Any) = out.println(obj)
    fun println(i: Int) = out.println(i)
    fun println(l: Long) = out.println(l)
    inline fun exec(block: IO.() -> Unit) {
        block()
        out.flush()
    }

    inline fun println(block: IO.() -> Any) {
        println(block())
        out.flush()
    }
}
// endregion