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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

function Main(arg) {
 
    var N = arg.split("\n")[0].split(" ")[0]-0;
    var K = arg.split("\n")[0].split(" ")[1]-0;
    var P = arg.split("\n")[1].split(" ").map(v => v-0);

    var ans = [];
    for (var i = 0; i < N - K + 1; i++){
        var tmp = P.slice(i, i + K);
        tmp.sort(compareNumbers);
        ans[i] = P.slice(0, i).concat(tmp).concat(P.slice(i + K)).toString();
    }

    var aa = new Set(ans);

    console.log(aa.size);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));