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: Accepted)

#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse4,popcnt,abm,mmx,tune=native")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
using namespace std;using namespace std::placeholders;using namespace __gnu_pbds;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define f first
#define s second
#define all(a) (a).begin(),(a).end()
#define For(i,a,b) for(auto i=(a);i<(b);i++)
#define FOR(i,b) For(i,0,b)
#define Rev(i,a,b) for(auto i=(a);i>(b);i--)
#define REV(i,a) Rev(i,a,-1)
#define FORE(i,a) for(auto&&i:a)
template<class C>constexpr int sz(const C&c){return int(c.size());}
using ll=long long;using ld=long double;using uint=unsigned int;using ull=unsigned long long;
using pii=pair<int,int>;using pll=pair<ll,ll>;using pill=pair<int,ll>;using plli=pair<ll,int>;using pdd=pair<double,double>;using pld=pair<ld,ld>;
constexpr const char nl='\n',sp=' ';constexpr const int INT_INF=0x3f3f3f3f;constexpr const ll LL_INF=0x3f3f3f3f3f3f3f3f;
constexpr const double D_INF=numeric_limits<double>::infinity();constexpr const ld LD_INF=numeric_limits<ld>::infinity();
template<class T>constexpr const T&_min(const T&x,const T&y){return x<y?x:y;}template<class T>constexpr const T&_max(const T&x,const T&y){return x<y?y:x;}
template<class T,class...Ts>constexpr const T&_min(const T&x,const Ts&...xs){return _min(x,_min(xs...));}
template<class T,class...Ts>constexpr const T&_max(const T&x,const Ts&...xs){return _max(x,_max(xs...));}
template<class T,class...Ts>void MIN(T&x,const Ts&...xs){x=_min(x,xs...);}template<class T,class...Ts>void MAX(T&x,const Ts&...xs){x=_max(x,xs...);}
template<class T>constexpr const T&_clamp(const T&v,const T&lo,const T&hi){return v<lo?lo:hi<v?hi:v;}template<class T>void CLAMP(T&v,const T&lo,const T&hi){v=_clamp(v,lo,hi);}
template<class T,class...Args>unique_ptr<T>_make_unique(Args&&...args){return unique_ptr<T>(new T(forward<Args>(args)...));}
template<class T,class...Args>shared_ptr<T>_make_shared(Args&&...args){return shared_ptr<T>(new T(forward<Args>(args)...));}
#define min(...) _min(__VA_ARGS__)
#define max(...) _max(__VA_ARGS__)
#define clamp(...) _clamp(__VA_ARGS__)
#define make_unique _make_unique
#define make_shared _make_shared
seed_seq seq {
    (uint64_t)chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count(),
    (uint64_t)__builtin_ia32_rdtsc(),(uint64_t)(uintptr_t)make_unique<char>().get()
};
mt19937 rng(seq);mt19937_64 rng64(seq);const size_t RANDOM=uniform_int_distribution<size_t>(0,(numeric_limits<size_t>::max)())(rng64);
template<class T,class H=hash<T>>struct rand_hash{
    static uint64_t splitmix64(uint64_t x){x+=0x9e3779b97f4a7c15;x=(x^(x>>30))*0xbf58476d1ce4e5b9;x=(x^(x>>27))*0x94d049bb133111eb;return x^(x>>31);}
    size_t operator()(const T&x)const{return splitmix64(H{}(x)+RANDOM);}
};
template<class K,class H=rand_hash<K>,class...Ts>using hashset=gp_hash_table<K,null_type,H,Ts...>;
template<class K,class V,class H=rand_hash<K>,class...Ts>using hashmap=gp_hash_table<K,V,H,Ts...>;
template<class K,class C=less<K>,class...Ts>using treeset=tree<K,null_type,C,rb_tree_tag,tree_order_statistics_node_update,Ts...>;
template<class K,class V,class C=less<K>,class...Ts>using treemap=tree<K,V,C,rb_tree_tag,tree_order_statistics_node_update,Ts...>;
template<class K,class H=rand_hash<K>,class...Ts>using uset=unordered_set<K,H,Ts...>;template<class K,class V,class H=rand_hash<K>,class...Ts>using umap=unordered_map<K,V,H,Ts...>;
template<class T>using minpq=std::priority_queue<T,vector<T>,greater<T>>;template<class T>using maxpq=std::priority_queue<T,vector<T>,less<T>>;
template<class T>using minpairingheap=__gnu_pbds::priority_queue<T,greater<T>,pairing_heap_tag>;template<class T>using maxpairingheap=__gnu_pbds::priority_queue<T,less<T>,pairing_heap_tag>;
template<class T1,class T2,class H1=rand_hash<T1>,class H2=rand_hash<T2>>struct pair_hash{size_t operator()(const pair<T1,T2>&p)const{return 31*H1{}(p.first)+H2{}(p.second);}};
template<class T>struct is_iterator {
    template<class U,typename enable_if<!is_convertible<U,const char*>::value,int>::type=0>constexpr static auto has_indirection(int)->decltype(*declval<U>(),bool()){return true;}
    template<class>constexpr static bool has_indirection(long){return false;}constexpr static bool value=has_indirection<T>(0);
};

#define INTERACTIVE_INPUT 0
constexpr const int _bufferSize=1<<16,_maxNumLength=128;
char _inputBuffer[_bufferSize+1],*_inputPtr=_inputBuffer,_outputBuffer[_bufferSize],_c,_sign,*_tempInputBuf=nullptr,_numBuf[_maxNumLength],_tempOutputBuf[_maxNumLength],_fill=' ';
FILE*_input=stdin,*_output=stdout,*_error=stderr;const char*_delimiter=" ";int _cur,_outputPtr=0,_numPtr=0,_precision=6,_width=0,_tempOutputPtr=0,_cnt;ull _precisionBase=1000000;
#ifdef _WIN32
    #define getchar_unlocked getchar
    #define fread_unlocked fread
    #define fwrite_unlocked fwrite
#endif
#if INTERACTIVE_INPUT
    #define _getchar() getchar_unlocked()
#else
    #define _peekchar() (*_inputPtr?*_inputPtr:(_inputBuffer[fread_unlocked(_inputPtr=_inputBuffer,1,_bufferSize,_input)]='\0',*_inputPtr))
    #define _getchar() (*_inputPtr?*_inputPtr++:(_inputBuffer[fread_unlocked(_inputPtr=_inputBuffer,1,_bufferSize,_input)]='\0',*_inputPtr++))
    #define _hasNext() (*_inputPtr||!feof(_input))
    bool hasNext(){while(_hasNext()&&_peekchar()<=' ')_getchar();return _hasNext();}bool hasNextLine(){while(_hasNext()&&_peekchar()=='\r')_getchar();return _hasNext();}
#endif
#define _readSignAndNum(x) while(((x)=_getchar())<=' ');_sign=(x)=='-';if(_sign)(x)=_getchar();for((x)-='0';(_c=_getchar())>='0';(x)=(x)*10+_c-'0')
#define _readFloatingPoint(x,T) for(T _div=1.0;(_c=_getchar())>='0';(x)+=(_c-'0')/(_div*=10))
#define rc(x) do{while(((x)=_getchar())<=' ');}while(0)
#define ri(x) do{_readSignAndNum(x);if(_sign)(x)=-(x);}while(0)
#define rd(x) do{_readSignAndNum(x);if(_c=='.')_readFloatingPoint(x,double);if(_sign)(x)=-(x);}while(0)
#define rld(x) do{_readSignAndNum(x);if(_c=='.')_readFloatingPoint(x,ld);if(_sign)(x)=-(x);}while(0)
#define rcs(x) do{_cur=0;do{_c=_getchar();}while(_c<=' ');do{(x)[_cur++]=_c;}while((_c=_getchar())>' ');(x)[_cur]='\0';}while(0)
#define rs(x) do{if(!_tempInputBuf)assert(0);rcs(_tempInputBuf);(x)=string(_tempInputBuf,_cur);}while(0)
#define rcln(x) do{while(_inputPtr!=_inputBuffer&&*(_inputPtr-1)=='\r')_getchar();_cur=0;while((_c=_getchar())!='\n'&&_c){if(_c!='\r')(x)[_cur++]=_c;}(x)[_cur]='\0';}while(0)
#define rln(x) do{if(!_tempInputBuf)assert(0);rcln(_tempInputBuf);(x)=string(_tempInputBuf,_cur);}while(0)
void setLength(int x){if(_tempInputBuf)delete[](_tempInputBuf);_tempInputBuf=new char[x+1];}
void read(int&x){ri(x);}void read(uint&x){ri(x);}void read(ll&x){ri(x);}void read(ull&x){ri(x);}void read(double&x){rd(x);}void read(ld&x){rld(x);}
void read(char&x){rc(x);}void read(char*x){rcs(x);}void read(string&x){rs(x);}void readln(char*x){rcln(x);}void readln(string&x){rln(x);}
template<class T1,class T2>void read(pair<T1,T2>&x){read(x.first);read(x.second);}template<class T>void read(complex<T>&x){T _re,_im;read(_re);read(_im);x.real(_re);x.imag(_im);}
template<class T>void read(T&x);template<class T,class...Ts>void read(T&x,Ts&&...xs);
template<class It>typename enable_if<is_iterator<It>::value>::type read(It st,It en){for(It _i=st;_i!=en;_i++)read(*_i);}
template<class It,class...Ts>typename enable_if<is_iterator<It>::value>::type read(It st,It en,Ts&&...xs){read(st,en);read(forward<Ts>(xs)...);}
template<class T>void read(T&x){for(auto&&_i:x)read(_i);}template<class T,class...Ts>void read(T&x,Ts&&...xs){read(x);read(forward<Ts>(xs)...);}
void setInput(FILE*file){*_inputPtr='\0';_input=file;}void setInput(const char*s){*_inputPtr='\0';_input=fopen(s,"r");}void setInput(const string&s){*_inputPtr='\0';_input=fopen(s.c_str(),"r");}
#define _flush() do{_flushBuf();fflush(_output);}while(0)
#define _flushBuf() (fwrite_unlocked(_outputBuffer,1,_outputPtr,_output),_outputPtr=0)
#define _putchar(x) (_outputBuffer[_outputPtr==_bufferSize?_flushBuf():_outputPtr]=(x),_outputPtr++)
#define _writeTempBuf(x) (_tempOutputBuf[_tempOutputPtr++]=(x))
#define _writeOutput() for(int _i=0;_i<_tempOutputPtr;_putchar(_tempOutputBuf[_i++]));_tempOutputPtr=0
#define _writeNum(x,T,digits) _cnt=0;for(T _y=(x);_y;_y/=10,_cnt++)_numBuf[_numPtr++]='0'+_y%10;for(;_cnt<digits;_cnt++)_numBuf[_numPtr++]='0';_flushNumBuf();
#define _writeFloatingPoint(x,T) ull _I=(ull)(x);ull _F=((x)-_I)*_precisionBase+(T)(0.5);if(_F>=_precisionBase){_I++;_F=0;}_writeNum(_I,ull,1);_writeTempBuf('.');_writeNum(_F,ull,_precision)
#define _checkFinite(x) if(std::isnan(x)){wcs("NaN");}else if(std::isinf(x)){wcs("Inf");}
#define _flushNumBuf() for(;_numPtr;_writeTempBuf(_numBuf[--_numPtr]))
#define _fillBuf(x) for(int _i=0;_i<(x);_i++)_putchar(_fill)
#define _flushTempBuf() int _tempLen=_tempOutputPtr;_fillBuf(_width-_tempLen);_writeOutput();_fillBuf(-_width-_tempLen)
#define wb(x) do{if(x)_writeTempBuf('1');else _writeTempBuf('0');_flushTempBuf();}while(0)
#define wc(x) do{_writeTempBuf(x);_flushTempBuf();}while(0)
#define wi(x) do{if((x)<0){_writeTempBuf('-');_writeNum(-(x),uint,1);}else{_writeNum(x,uint,1);}_flushTempBuf();}while(0)
#define wll(x) do{if((x)<0){_writeTempBuf('-');_writeNum(-(x),ull,1);}else{_writeNum(x,ull,1);}_flushTempBuf();}while(0)
#define wd(x) do{_checkFinite(x)else if((x)<0){_writeTempBuf('-');_writeFloatingPoint(-(x),double);}else{_writeFloatingPoint(x,double);}_flushTempBuf();}while(0)
#define wld(x) do{_checkFinite(x)else if((x)<0){_writeTempBuf('-');_writeFloatingPoint(-(x),ld);}else{_writeFloatingPoint(x,ld);}_flushTempBuf();}while(0)
#define wcs(x) do{int _slen=strlen(x);_fillBuf(_width-_slen);for(const char*_p=(x);*_p;_putchar(*_p++));_fillBuf(-_width-_slen);}while(0)
#define ws(x) do{_fillBuf(_width-int((x).length()));for(int _i=0;_i<int((x).length());_putchar(x[_i++]));_fillBuf(-_width-int((x).length()));}while(0)
void setPrecision(int x){_precision=x;_precisionBase=1;for(int _i=0;_i<x;_i++,_precisionBase*=10);}void setWidth(int x){_width=x;}void setFill(char x){_fill=x;}
void setDelimiter(const char*x){_delimiter=x;}void setDelimiter(const string&x){_delimiter=x.c_str();}
void writeDelimiter(){for(const char*_p=_delimiter;*_p;_putchar(*_p++));}
void write(const bool&x){wb(x);}void write(const int&x){wi(x);}void write(const uint&x){wi(x);}void write(const ll&x){wll(x);}void write(const ull&x){wll(x);}
void write(const double&x){wd(x);}void write(const ld&x){wld(x);}void write(const char&x){wc(x);}void write(const char*x){wcs(x);}void write(const string&x){ws(x);}
template<class T1,class T2>void write(const pair<T1,T2>&x){write(x.first);writeDelimiter();write(x.second);}
template<class T>void write(const complex<T>&x){write(x.real());writeDelimiter();write(x.imag());}
template<class T>void write(const T&x);template<class T,class...Ts>void write(const T&x,Ts&&...xs);
template<class It>typename enable_if<is_iterator<It>::value>::type write(It st,It en){bool _first=1;for(It _i=st;_i!=en;_i++){if(_first)_first=0;else writeDelimiter();write(*_i);}}
template<class It,class...Ts>typename enable_if<is_iterator<It>::value>::type write(It st,It en,Ts&&...xs){write(st,en);writeDelimiter();write(forward<Ts>(xs)...);}
template<class T>void write(const T&x){bool _first=1;for(auto&&_i:x){if(_first)_first=0;else writeDelimiter();write(_i);}}
template<class T,class...Ts>void write(const T&x,Ts&&...xs){write(x);writeDelimiter();write(forward<Ts>(xs)...);}
void writeln(){_putchar('\n');}template<class...Ts>void writeln(Ts&&...xs){write(forward<Ts>(xs)...);_putchar('\n');}
void flush(){_flush();}class IOManager{public:~IOManager(){flush();if(_tempInputBuf)delete[](_tempInputBuf);}};unique_ptr<IOManager>iomanager=make_unique<IOManager>();
void setOutput(FILE*file){flush();_output=file;}void setOutput(const char*s){flush();_output=fopen(s,"w");}void setOutput(const string&s){flush();_output=fopen(s.c_str(),"w");}
template<class...Ts>void debug(const Ts&...xs){FILE*_temp=_output;setOutput(_error);write(xs...);setOutput(_temp);}
template<class...Ts>void debugln(const Ts&...xs){FILE*_temp=_output;setOutput(_error);writeln(xs...);setOutput(_temp);}
void setError(FILE*file){flush();_error=file;}void setError(const char*s){flush();_error=fopen(s,"w");}void setError(const string&s){flush();_error=fopen(s.c_str(),"w");}

const int MAXN = 2e5 + 5, MAXLGN = 22;

int LG[MAXN];

template <const int MAXN, const int MAXLGN, class T, const bool IS_MAX> struct SparseTableRMQ {
    T A[MAXN]; int ST[MAXLGN][MAXN];
    int cmpInd(int l, int r) { return (A[l] <= A[r]) ^ IS_MAX ? l : r; }
    void init(int N) {
        int lg = LG[N] + 1; assert(lg < MAXLGN); iota(ST[0], ST[0] + N, 0);
        for (int i = 0; i < lg - 1; i++) for (int j = 0; j + (1 << i) < N; j++) ST[i + 1][j] = cmpInd(ST[i][j], ST[i][j + (1 << i)]);
    }
    // 0-indexed, inclusive
    int query(int l, int r) { int i = LG[r - l + 1]; return cmpInd(ST[i][l], ST[i][r - (1 << i) + 1]); }
};

int N, K, P[MAXN], D[MAXN];
SparseTableRMQ<MAXN, MAXLGN, int, 1> MX;
SparseTableRMQ<MAXN, MAXLGN, int, 0> MN;

int main() {
    // setInput("in.txt");
    // setOutput("out.txt");
    // setError("err.txt");
    read(N, K);
    if (K == 1) {
        writeln(N);
        return 0;
    } else if (K == N) {
        writeln(1);
        return 0;
    }
    LG[0] = LG[1] = 0;
    For(i, 2, N + 1) LG[i] = LG[i / 2] + 1;
    read(P, P + N);
    copy(P, P + N, MX.A);
    MX.init(N);
    copy(P, P + N, MN.A);
    MN.init(N);
    adjacent_difference(P, P + N, D);
    int ans = 0, hasNoSort = 0, cur = 0;
    For(i, 1, K) cur += D[i] > 0;
    if (cur == K - 1) hasNoSort = 1;
    else ans = 1;
    FOR(i, N - K) {
        cur -= D[i + 1] > 0;
        cur += D[i + K] > 0;
        if (cur == K - 1) hasNoSort = 1;
        else if (i != MN.query(i, i + K - 1) || i + K != MX.query(i + 1, i + K)) ans++;
    }
    writeln(ans + hasNoSort);
    return 0;
}