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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// #define DEBUGGING
#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define ALL(V) (V).begin(), (V).end()
#define ALLR(V) (V).rbegin(), (V).rend()

template <typename T> using V = vector<T>;
template <typename T> using VV = V<V<T>>;
using ll = int64_t;
using ull = uint64_t;
using PLL = pair<ll, ll>;

template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return max(t, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }
template <typename T> const T& clamp(const T &t, const T &low, const T &high) { return max(low, min(high, t)); }
template <typename T> void chclamp(T &t, const T &low, const T &high) { t = clamp(t, low, high); }

namespace init__ {

struct InitIO {
    InitIO() {
        cin.tie(nullptr);
        ios_base::sync_with_stdio(false);
        cout << fixed << setprecision(30);
    }
} init_io;

}

#ifdef DEBUGGING
// #include "../debug/debug.cpp"
#include "../../debug/debug.cpp"
#else
#define DEBUG(...) 0
#define DEBUG_SEPARATOR_LINE 0
#endif

template <typename T>
T make_v(T init) { return init; }

template <typename T, typename... Tail>
auto make_v(T init, size_t s, Tail... tail) {
#define rec make_v(init, tail...)
    return V<decltype(rec)>(s, rec);
#undef rec
}

template <typename T>
class SegmentTree {
public:
    ll size;
    vector<T> node;
    function<T(T, T)> comp;
    T identity_ele;  //comp(x, identity_ele) == x

    SegmentTree(const vector<T> v, function<T(T, T)> comp, T identity_ele) 
        : comp(comp),
          identity_ele(identity_ele)
    {
        ll tmp = 1;
        while(tmp < v.size()) tmp = (tmp << 1);
        this->size = tmp;
        this->identity_ele = identity_ele;
        this->comp = comp;
        node = V<T>(2 * size - 1, identity_ele);
        for(ll i = 0; i < v.size(); i++) {
            node[i + size - 1] = v[i];
        }
        for(ll i = size - 2; 0 <= i; i--) {
            node[i] = comp(node[i * 2 + 1], node[i * 2 + 2]);
        }
    }

    void update(ll pos, T value) {
        pos += size - 1;
        node[pos] = value;
        while(pos > 0) {
            pos = (pos - 1) / 2;
            node[pos] = comp(node[2 * pos + 1], node[2 * pos + 2]);
        }
    }

    T query(ll a, ll b) {
        return sub_query(a, b, 0, 0, size);
    }

    T sub_query(ll a, ll b, ll k, ll l, ll r) {
        if(r <= a || b <= l) {
            return identity_ele;
        } else if(a <= l && r <= b) {
            return node[k];
        } else {
            T left = sub_query(a, b, k * 2 + 1, l, (l + r) / 2);
            T right = sub_query(a, b, k * 2 + 2, (l + r) / 2, r);
            return comp(left, right);
        }
    }
};

int main() {
    ll N, K;
    cin >> N >> K;
    V<ll> P(N);
    for(auto &&ele : P) cin >> ele;

    SegmentTree<ll> st_max(V<ll>(N + 10), [](ll a, ll b) { return max(a, b); }, -1);
    SegmentTree<ll> st_min(V<ll>(N + 10), [](ll a, ll b) { return min(a, b); }, N + 10);
    
    ll ans = 1;

    ll cnt_perm = 0;
    {
        ll idx = 0;
        while(idx < N) {
            ll store = idx;
            while(idx < N - 1 && P[idx] < P[idx + 1]) idx++;
            DEBUG(PLL(idx, store));
            cnt_perm += (idx - store + 1 >= K);
            idx++;
        }
    }

    for(ll i = 0; i < K; i++) {
        st_max.update(P[i], P[i]);
        st_min.update(P[i], P[i]);
    }

    for(ll i = 1; i <= N - K; i++) {
        ll pre_left = P[i - 1];
        ll right = P[i + K - 1];
        st_max.update(pre_left, 0);
        st_min.update(pre_left, 0);
        DEBUG(ans);
        DEBUG(make_tuple(right, st_min.query(0, N + 10), st_max.query(0, N + 10)));
        ll add_v = 0;
        if(pre_left > st_min.query(i, N + 10)) add_v = 1;
        if(right < st_max.query(i, N + 10)) add_v = 1;
        st_max.update(right, right);
        st_min.update(right, right);
        DEBUG(PLL(i, ans));
        ans += add_v;
    }

    DEBUG(cnt_perm);
    if(cnt_perm >= 2) ans--;
    cout << ans << endl;
    return 0;
}