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:
import heapq

N,K = map(int, input().split())
P = [int(p) for p in input().split()]

h = []
H = []
for i in range(K):
    heapq.heappush(h, (P[i], i))
    heapq.heappush(H, (-P[i], i))
    
ans = 1
for i in range(N-K):
    while h[0][1] < i:
        heapq.heappop(h)
    while H[0][1] < i:
        heapq.heappop(H)
    heapq.heappush(h, (P[i+K], i+K))
    heapq.heappush(H, (-P[i+K], i+K))
    if h[0][0] == P[i] and -H[0][0] == P[i+K]:
        continue
    ans += 1
    
f = 0
cnt = 1
for i in range(N-1):
    if P[i] < P[i+1]:
        cnt += 1
    else:
        if cnt >= K and f == 1:
            ans -= 1
        elif cnt >= K and f == 0:
            f = 1
        cnt = 1
        
if cnt >= K and f == 1:
    ans -= 1
    
print(ans)