Problem: 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.

Examples

Input

5 3
0 2 1 4 3


Output

2


Input

4 4
0 1 2 3


Output

1


Input

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


Output

6

Solution (in PYTHON3):

Solution:
from collections import deque
def slidemax(X, k):
    q = deque([])
    ret = []
    for i in range(len(X)):
        while q and q[-1][1] <= X[i]:
            q.pop()
        deque.append(q, (i+k, X[i]))
        if q[0][0] == i:
            deque.popleft(q)
        if i >= k-1:
            ret.append(q[0][1])
    return ret

def slidemin(X, k):
    q = deque([])
    ret = []
    for i in range(len(X)):
        while q and q[-1][1] >= X[i]:
            q.pop()
        deque.append(q, (i+k, X[i]))
        if q[0][0] == i:
            deque.popleft(q)
        if i >= k-1:
            ret.append(q[0][1])
    return ret

N, K = map(int, input().split())
A = [int(a) for a in input().split()]

a = 0
l = -1
cnt = 0
for i in range(1, N):
    if A[i-1] > A[i]: a = i
    if i >= K-1 and a <= i - K + 1:
        if i - l > 1: cnt += 1
        l = i

MA = slidemax(A, K)
MI = slidemin(A, K)
ans = 1 - max(cnt-1, 0)
l = -1
for i in range(K, N):
    if MI[i-K] != A[i-K] or MA[i-K+1] != A[i]:
        ans += 1

print(ans)