#line 1 "graph_tree/test/LC_min_cost_flow.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/min_cost_b_flow"
#line 2 "util/template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
#include<bits/stdc++.h>
using namespace std;
struct __INIT__{__INIT__(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}}__INIT__;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define endl ('\n')
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>using V=vector<T>;
template<typename T>using VV=V<V<T>>;
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void debug(T t){bool f=0;for(auto i:t){cerr<<(f?" ":"")<<i;f=1;}cerr<<endl;}
template<typename T>inline void debug2(T t){for(auto i:t)output(i);}
#define loop(n) for(long long _=0;_<(long long)(n);++_)
#define _overload4(_1,_2,_3,_4,name,...) name
#define __rep(i,a) repi(i,0,a,1)
#define _rep(i,a,b) repi(i,a,b,1)
#define repi(i,a,b,c) for(long long i=(long long)(a);i<(long long)(b);i+=c)
#define rep(...) _overload4(__VA_ARGS__,repi,_rep,__rep)(__VA_ARGS__)
#define _overload3_rev(_1,_2,_3,name,...) name
#define _rep_rev(i,a) repi_rev(i,0,a)
#define repi_rev(i,a,b) for(long long i=(long long)(b)-1;i>=(long long)(a);--i)
#define rrep(...) _overload3_rev(__VA_ARGS__,repi_rev,_rep_rev)(__VA_ARGS__)
// #define rep(i,...) for(auto i:range(__VA_ARGS__))
// #define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__)))
// #define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
// #define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
// #define irep(i) for(lint i=0;;++i)
// inline vector<long long> range(long long n){if(n<=0)return vector<long long>();vector<long long>v(n);iota(v.begin(),v.end(),0LL);return v;}
// inline vector<long long> range(long long a,long long b){if(b<=a)return vector<long long>();vector<long long>v(b-a);iota(v.begin(),v.end(),a);return v;}
// inline vector<long long> range(long long a,long long b,long long c){if((b-a+c-1)/c<=0)return vector<long long>();vector<long long>v((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;}
// template<typename T>inline T reversed(T v){reverse(v.begin(),v.end());return v;}
#define all(n) begin(n),end(n)
template<typename T,typename E>bool chmin(T& s,const E& t){bool res=s>t;s=min<T>(s,t);return res;}
template<typename T,typename E>bool chmax(T& s,const E& t){bool res=s<t;s=max<T>(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
#define extrep(v,...) for(auto v:__MAKE_MAT__({__VA_ARGS__}))
#define bit(n,a) ((n>>a)&1)
vector<vector<long long>> __MAKE_MAT__(vector<long long> v){if(v.empty())return vector<vector<long long>>(1,vector<long long>());long long n=v.back();v.pop_back();vector<vector<long long>> ret;vector<vector<long long>> tmp=__MAKE_MAT__(v);for(auto e:tmp)for(long long i=0;i<n;++i){ret.push_back(e);ret.back().push_back(i);}return ret;}
using graph=vector<vector<int>>;
template<typename T>using graph_w=vector<vector<pair<int,T>>>;
template<typename T,typename E>ostream& operator<<(ostream& out,pair<T,E>v){out<<"("<<v.first<<","<<v.second<<")";return out;}
constexpr inline long long powll(long long a,long long b){long long res=1;while(b--)res*=a;return res;}
#line 6 "graph_tree/push_relabel.hpp"
/**
* @brief 最大流(push_relabel法O(V^2√E))
*/
template<typename T>
class push_relabel{
int n;
T f=0;
using i64=long long;
struct edge{
int from,to,rev;
T flow,cap;
};
std::vector<i64>h,d;
std::vector<std::vector<edge*>>g;
std::vector<size_t>seen;
std::priority_queue<std::pair<i64,int>,std::vector<std::pair<i64,int>>,std::greater<std::pair<i64,int>>>que;
public:
push_relabel(int n):n(n){
h.resize(n,0);
d.resize(n,0);
g.resize(n);
seen.resize(n,0);
}
void add_edge(int u,int v,T cap){
g[u].emplace_back(new edge{u,v,(int)g[v].size(),0,cap});
g[v].emplace_back(new edge{v,u,(int)g[u].size()-1,0,0});
}
void push(edge* e){
int u=e->from,v=e->to;
i64 df=std::min(d[u],e->cap-e->flow);
e->flow+=df;
g[v][e->rev]->flow-=df;
d[u]-=df;
d[v]+=df;
if(d[v]>0)que.emplace(h[v],v);
if(d[u]>0)que.emplace(h[u],u);
}
void relabel(int u){
i64 mn=n*2;
for(edge* e:g[u]){
if(e->cap-e->flow>0){
mn=std::min(mn,h[e->to]);
}
}
h[u]=1+mn;
que.emplace(h[u],u);
}
void discharge(int u){
while(d[u]>0){
if(seen[u]<g[u].size()){
edge* e=g[u][seen[u]];
if(e->cap-e->flow>0 && h[u]==h[e->to]+1){
push(e);
}else{
seen[u]+=1;
}
}else{
relabel(u);
seen[u]=0;
}
}
}
T run(int s,int t){
h[s]=n;
for(auto e:g[s]){
d[s]+=e->cap;
push(e);
}
while(!que.empty()){
int u=que.top().second;
que.pop();
if(u==s||u==t)continue;
discharge(u);
}
for(auto e:g[s])f+=e->flow;
return f;
}
};
#line 6 "graph_tree/min_cost_flow.hpp"
/**
* @brief 最小費用流(CostScaling)
*/
//Resは答えがlong longの最大値を超える時用
template<typename T,typename Res=T>
struct min_cost_flow{
int v;
Res ans=0;
struct edge{
int to;
T cap,cost,st;
int rev;
bool is_rev,edge_rev;
int id;
};
push_relabel<T> mf;
std::vector<T>p;
std::vector<vector<edge*>>e;//辺のキャパシティ
std::vector<T>d;//頂点のキャパシティ
std::queue<int>active;
std::vector<tuple<int,int,T,T,T>>edges;
T eps=1;
int idx=0;
std::vector<T>res;
min_cost_flow(int v):v(v),mf(v+2),p(v,0),e(v),d(v,0){}
void add_edge(int from,int to,T mn,T mx,T cost){
edges.emplace_back(from,to,mn,mx,cost);
res.push_back(0);
if(from==to){
if(cost<0)res[idx++]=mx,ans+=mx*cost;
else res[idx++]=mn,ans+=mn*cost;
return;
}
if(cost>=0){
e[from].push_back(new edge{to,mx-mn,cost*v,mn,(int)e[to].size(),0,0,idx});
e[to].push_back(new edge{from,0,-cost*v,mn,(int)e[from].size()-1,1,0,idx++});
ans+=mn*cost;
d[from]-=mn;d[to]+=mn;
eps=max(eps,cost*v*v);
mf.add_edge(from,to,mx-mn);
}
else{
e[to].push_back(new edge{from,mx-mn,-cost*v,mx,(int)e[from].size(),0,1,idx});
e[from].push_back(new edge{to,0,cost*v,mx,(int)e[to].size()-1,1,1,idx++});
ans+=mx*cost;
d[from]-=mx;d[to]+=mx;
eps=max(eps,-cost*v*v);
mf.add_edge(to,from,mx-mn);
}
}
void add_edge(int from,int to,T cap,T cost){
add_edge(from,to,T(),cap,cost);
}
Res flow(){
for(;eps;eps>>=1){
for(int i=0;i<v;i++){
for(auto ed:e[i]){
if(ed->is_rev)continue;
if(ed->cost-p[i]+p[ed->to]<0){
T f=ed->cap;
ed->cap-=f;
d[i]-=f;
d[ed->to]+=f;
e[ed->to][ed->rev]->cap+=f;
}
if(ed->cost-p[i]+p[ed->to]>0){
T f=-e[ed->to][ed->rev]->cap;
ed->cap-=f;
d[i]-=f;
d[ed->to]+=f;
e[ed->to][ed->rev]->cap+=f;
}
}
}
for(int i=0;i<v;i++)if(d[i]>0){active.emplace(i);}
while(!active.empty()){
int node=active.front();
active.pop();
if(d[node]<=0)continue;
bool b=0;
for(auto ed:e[node]){
if(!d[node])break;
if(-eps<=ed->cost-p[node]+p[ed->to]&&ed->cost-p[node]+p[ed->to]<0){
auto f=std::min(d[node],ed->cap);
if(!f)continue;
ed->cap-=f;
d[node]-=f;
d[ed->to]+=f;
e[ed->to][ed->rev]->cap+=f;
if(d[ed->to]>0)active.emplace(ed->to);
b=1;
}
}
if(d[node]>0)active.emplace(node);
if(!b)p[node]+=eps;
}
}
for(int i=0;i<v;i++)for(auto ed:e[i]){
if(ed->is_rev)continue;
ans+=e[ed->to][ed->rev]->cap*(ed->cost/v);
}
return ans;
}
bool ok(std::vector<T>b){
T tmp=0,tmp2=0;
for(int i=0;i<v;++i){
if(d[i]+b[i]>=0){
mf.add_edge(v,i,d[i]+b[i]);
tmp2+=d[i]+b[i];
}
else{
mf.add_edge(i,v+1,-(d[i]+b[i]));
tmp+=-(d[i]+b[i]);
}
}
return tmp==tmp2&&mf.run(v,v+1)==tmp;
}
Res run(int s,int t,T f){
d[s]+=f;
d[t]-=f;
return flow();
}
Res run(std::vector<T>b){
for(int i=0;i<v;++i)d[i]+=b[i];
return flow();
}
std::vector<T> flow_result(){
for(int i=0;i<v;i++)for(auto ed:e[i]){
if(ed->is_rev)continue;
res[ed->id]=ed->st+e[ed->to][ed->rev]->cap*(ed->edge_rev?-1:1);
}
return res;
}
//flow_resultを渡す
std::vector<T>potential(const std::vector<T>& f){
std::vector<T>p(v,0);
std::vector<tuple<int,int,T>>g;
int idx=0;
for(auto [from,to,mn,mx,cost]:edges){
if(mn<f[idx])g.emplace_back(to,from,-cost);
if(f[idx]<mx)g.emplace_back(from,to,cost);
idx++;
}
for(int i=0;i<v;++i)for(auto [s,t,c]:g){
p[t]=std::min(p[t],p[s]+c);
}
return p;
}
};
#line 1 "util/int128.hpp"
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
std::ostream::sentry s(dest);
if(s){
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
__int128 parse(string &s) {
__int128 ret = 0;
for (int i = 0; i < (int)s.length(); i++)
if ('0' <= s[i] && s[i] <= '9')
ret = 10 * ret + s[i] - '0';
return ret;
}
std::istream &operator>>(std::istream &dest, __int128_t& value){
string s;
dest>>s;
value=parse(s);
return dest;
}
#line 5 "graph_tree/test/LC_min_cost_flow.test.cpp"
int main(){
lint n,m;
cin>>n>>m;
vector<lint>b(n);
rep(i,n){
lint x;
cin>>x;
b[i]=x;
}
min_cost_flow<lint,__int128_t> mf(n);
loop(m){
lint from,to,l,r,cost;
cin>>from>>to>>l>>r>>cost;
mf.add_edge(from,to,l,r,cost);
}
if(mf.ok(b)){
cout<<mf.run(b)<<endl;
auto f=mf.flow_result();
auto p=mf.potential(f);
rep(i,n){
cout<<p[i]<<endl;
}
rep(i,m){
cout<<f[i]<<endl;
}
}
else cout<<"infeasible"<<endl;
}
graph_tree/test/LC_min_cost_flow.test.cpp