Problem Link : https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1031
Solution Idea: first check if it is possible or not to get a valid result. If possible then get one result with extended euclid algo and then check the result taking minimum type 1 box and then check the result taking minimum type 2 box. print the minimum value.
#include <bits/stdc++.h>
#define pii pair <int,int>
#define pll pair <long long,long long>
#define sc scanf
#define pf printf
#define Pi 2*acos(0.0)
#define ms(a,b) memset(a, b, sizeof(a))
#define pb(a) push_back(a)
#define MP make_pair
#define db double
#define ll long long
#define EPS 10E-10
#define ff first
#define ss second
#define sqr(x) (x)*(x)
#define D(x) cout<<#x " = "<<(x)<<endl
#define VI vector <int>
#define DBG pf("Hi\n")
#define MOD 1000000007
#define CIN ios_base::sync_with_stdio(0); cin.tie(0);cout.tie(0)
#define SZ(a) (int)a.size()
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v) for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define RREP(i,a,b) for(int i=a;i>=b;i--)
#define TEST_CASE(t) for(int z=1;z<=t;z++)
#define PRINT_CASE printf("Case %d: ",z)
#define CASE_PRINT cout<<"Case "<<z<<": "
#define all(a) a.begin(),a.end()
#define intlim 2147483648
#define infinity (1<<28)
#define ull unsigned long long
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
using namespace std;
/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*------------------------------------------------*/
/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/
ll extended_euclid(ll a, ll b, ll &x, ll &y)
{
if(b==0)
{
x=1,y=0;
return a;
}
ll x1,y1;
ll ret=extended_euclid(b,a%b,x1,y1);
x=y1;
y=x1-y1*(a/b);
return ret;
}
int main()
{
CIN;
// freopen("in.txt","r",stdin);
///freopen("out.txt","w",stdout);
ll n;
while(cin>>n && n)
{
ll c1,n1,c2,n2;
cin>>c1>>n1>>c2>>n2;
bool test=0;
if(n % __gcd(n1,n2))
{
cout<<"failed"<<endl;
}
else
{
ll x,y;
ll gcdd=extended_euclid(n1,n2,x,y);
x*=(n/gcdd);
y*=(n/gcdd);
n1/=gcdd;
n2/=gcdd;
ll aa=ceil(-(double)x/n2);
ll bb=floor((double)y/n1);
if(aa<=bb)
{
if(c1 * (x + n2 * aa) + c2 * (y- n1*aa) < c1*(x+(n2*bb)) + c2*(y-n1*bb))
{
x+=n2*aa;
y-=n1*aa;
}
else
{
x+=n2*bb;
y-=n1*bb;
}
}
else
test=1;
if(test)
cout<<"failed"<<endl;
else
cout<<x<<" "<<y<<endl;
}
}
return 0;
}