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


def main():
    N, K = map(int, input().split())
    P = list(map(int, input().split()))
    ans = 1
    inside_que = [0] * N
    min_que, max_que = [], []
    for i in range(K):
        heapq.heappush(min_que, P[i])
        heapq.heappush(max_que, - P[i])
        inside_que[P[i]] = 1
    for i in range(N - K):
        old_p, new_p = P[i], P[i + K]
        if not(old_p == min_que[0] and new_p >= - max_que[0]):
            ans += 1
        inside_que[old_p] = 0
        inside_que[new_p] = 1
        heapq.heappush(min_que, new_p)
        heapq.heappush(max_que, - new_p)
        while inside_que[min_que[0]] == 0:
            heapq.heappop(min_que)
        while inside_que[-max_que[0]] == 0:
            heapq.heappop(max_que)
    desc_index = 0
    exists_asc_section = False
    for i in range(1, N):
        if P[i - 1] > P[i]:
            if i - desc_index >= K:
                ans -= 1
                exists_asc_section = True
            desc_index = i
    if N - desc_index >= K:
        exists_asc_section = True
        ans -= 1
    if exists_asc_section:
        ans += 1
    print(ans)


if __name__ == '__main__':
    main()