Problem: Example

Input

1 1 1 1 1


Output

0.000000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#include <type_traits>
using namespace std;

using ll=int64_t;
//#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define REP(i,b) FOR(i,0,b)
#define MP make_pair
#define PB push_back
#define EB emplace_back
#define ALL(x) x.begin(),x.end()
auto& errStream=cerr;
#ifdef LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define REACH cerr<<"reached"<<endl
#define DMP(x) cerr<<#x<<":"<<x<<endl
#define ZERO(x) memset(x,0,sizeof(x))
#define ONE(x) memset(x,-1,sizeof(x))

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"{";
	REP(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

ll read(){
	ll i;
	scanf("%"  SCNd64,&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%" PRId64,x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

string readString(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(b<a)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

#define CAPITAL
void Yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void No(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int gcd(int a,int b){
	return b?gcd(b,a%b):a;
}

int lcm(int a,int b){
	return a/gcd(a,b)*b;
}

int extgcd(int a,int b,int&x,int&y){
	if(b==0){
		x=1;
		y=0;
		return a;
	}else{
		int g=extgcd(b,a%b,y,x);
		y-=a/b*x;
		return g;
	}
}

signed main(){
	int w=read(),d=read(),n=read(),m=read(),t=read();
	int g,x,y;
	g=extgcd(m,t,x,y);
	int f=t/g;
	if(x<0)x+=f;
	assert(x>=0);
	int e=gcd(t,w+d);
	int cur=0;
	int cnt=0;
	int remG=0,remE=0;
	int last=-1;
	REP(i,t){
		if(remG==0){
			if(cur<n)last=i;
			cur+=x;
			if(cur>=f)cur-=f;
			remG=g-1;
		}else{
			remG--;
		}
		if(remE==0){
			cnt+=(last<i-w);
			remE=e-1;
		}else{
			remE--;
		}
	}
	cout<<fixed<<setprecision(20)<<double(cnt)/(t/e)<<endl;
}