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 heapq import heappush, heappop
import sys
input = sys.stdin.readline

N, K = map(int, input().split())
P = list(map(int, input().split()))
mn = [N] * (N-K)
mx = [-1] * (N-K)
min_heap = []
max_heap = []
for i in range(K):
    heappush(min_heap, P[i])
    heappush(max_heap, -P[i])
used = set()
for i in range(N-K):
    heappush(min_heap, P[i+K])
    heappush(max_heap, -P[i+K])
    while min_heap[0] in used:
        heappop(min_heap)
    while -max_heap[0] in used:
        heappop(max_heap)
    mn[i] = min_heap[0]
    mx[i] = -max_heap[0]
    used.add(P[i])
ans = 1
for i in range(N-K):
    if P[i] != mn[i] or P[i+K] != mx[i]:
        ans += 1
inc = 1
cnt = 0
for i in range(1, N):
    if P[i-1] < P[i]:
        inc += 1
    else:
        inc = 1
    if inc == K:
        cnt += 1
ans -= max(0, cnt-1)
print(ans)