P5481 [BJOI2015] 糖果

#include<bits/stdc++.h>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define W while
#define I inline
#define RI register int
#define LL long long
#define Cn const
#define CI Cn int&
#define gc getchar
#define D isdigit(c=gc())
#define pc(c) putchar((c))
#define min(x,y) ((x)<(y)?(x):(y))
#define max(x,y) ((x)>(y)?(x):(y))
using namespace std;
namespace Debug{
    Tp I void _debug(Cn char* f,Ty t){cerr<<f<<'='<<t<<endl;}
    Ts I void _debug(Cn char* f,Ty x,Ar... y){W(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
    Tp ostream& operator<<(ostream& os,Cn vector<Ty>& V){os<<"[";for(Cn auto& vv:V) os<<vv<<",";os<<"]";return os;}
    #define gdb(...) _debug(#__VA_ARGS__,__VA_ARGS__)
}using namespace Debug;
namespace FastIO{
    Tp I void read(Ty& x){char c;int f=1;x=0;W(!D) f=c^'-'?1:-1;W(x=(x<<3)+(x<<1)+(c&15),D);x*=f;}
    Ts I void read(Ty& x,Ar&... y){read(x),read(y...);}
    Tp I void write(Ty x){x<0&&(pc('-'),x=-x,0),x<10?(pc(x+'0'),0):(write(x/10),pc(x%10+'0'),0);}
    Tp I void writeln(Cn Ty& x){write(x),pc('\n');}
}using namespace FastIO;
Cn int N=2e9+1e5+10,M=sqrt(N);
int n,m,k,P,p[M],v[M],tot,y[M];
map<int,int> r;
I void GP(){
    RI i,j;for(i=2;i<M;i++) for(!v[i]&&(p[++tot]=i),j=1;j<=tot&&i*p[j]<M;j++)
    if(v[i*p[j]]=1,!(i%p[j])) break ; 
}
I void U(RI x,CI c){
    RI i;for(i=1;i<=tot&&p[i]<=x;i++) if(!(x%p[i])){
        W(!(x%p[i])) y[i]+=c,x/=p[i];
    }if(x>1) r[x]+=c;
}
I int QP(RI A,RI B){RI S=1;W(B) B&1&&(S=1LL*S*A%P),A=1LL*A*A%P,B>>=1;return S;}
I int G(){
    RI i,X=1;for(i=1;i<=tot;i++) X=1LL*X*QP(p[i],y[i])%P;
    for(auto j:r) X=1LL*X*QP(j.first,j.second)%P;return X;
}
int main(){
    RI i,X,Y=1;for(GP(),read(n,m,k,P),i=k;i<=m+k-1;i++) U(i,1);
    for(i=m;i>=1;i--) U(i,-1);for(X=G(),i=X-n+1;i<=X;i++) Y=1LL*Y*i%P;
    return writeln(Y),0;
}