There are n reindeer at the North Pole, all battling for the highest spot on the "Top Reindeer" leaderboard on the front page of CodeNorses (a popular competitive reindeer gaming website). Interestingly, the "Top Reindeer" title is just a measure of upvotes and has nothing to do with their skill level in the reindeer games, but they still give it the utmost importance.

Currently, the i-th reindeer has a score of a_i. You would like to influence the leaderboard with some operations. In an operation, you can choose a reindeer, and either increase or decrease his score by 1 unit. Negative scores are allowed.

You have m requirements for the resulting scores. Each requirement is given by an ordered pair (u, v), meaning that after all operations, the score of reindeer u must be less than or equal to the score of reindeer v.

Your task is to perform the minimum number of operations so that all requirements will be satisfied.

Input

The first line contains two integers n and m (2≤ n≤ 1000; 1≤ m≤ 1000) — the number of reindeer and requirements, respectively.

The second line contains n integers a_1,…, a_n (1≤ a_i≤ 10^9), where a_i is the current score of reindeer i.

The next m lines describe the requirements.

The i-th of these lines contains two integers u_i and v_i (1≤ u_i, v_i≤ n; u_i≠ v_i) — the two reindeer of the i-th requirement.

Output

Print n integers b_1,…, b_n (-10^{15}≤ b_i≤ 10^{15}), where b_i is the score of the i-th reindeer after all operations.

If there are multiple solutions achieving the minimum number of operations, you may output any.

We can prove that there is always an optimal solution such that |b_i|≤ 10^{15} for all i.

Examples

Input


7 6
3 1 4 9 2 5 6
1 2
2 3
3 4
4 5
5 6
6 7


Output


1 1 4 4 4 5 6 


Input


4 6
6 5 8 2
3 1
4 1
3 2
1 2
2 3
3 1


Output


6 6 6 2 


Input


10 18
214 204 195 182 180 176 176 172 169 167
1 2
3 2
4 2
5 2
6 2
7 2
8 2
9 2
10 2
6 1
6 2
6 3
6 4
6 5
6 7
6 8
6 9
6 10


Output


204 204 195 182 180 167 176 172 169 167 
2 1
1 1000000000
1 2
 2 1
1 1
1 2

1 1000000000 
 1 1 

//#define _GLIBCXX_DEBUG

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

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T> using PQ = priority_queue<T>;
template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};  
template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
  auto tmp = v;
  for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
  rearrange(ord, head);
  rearrange(ord, tail...);
}
template<typename T> vector<int> ascend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return v[i]<v[j];});
  return ord;
}
template<typename T> vector<int> descend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return v[i]>v[j];});
  return ord;
}
ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
ll modulo(ll n,ll d){return (n%d+d)%d;};
template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
template< typename T = int >
struct edge {
  int to;
  T cost;
  int id;
  edge():id(-1){};
  edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
  operator int() const { return to; }
};

template<typename T>
using Graph = vector<vector<edge<T>>>;
template<typename T>
Graph<T>revgraph(const Graph<T> &g){
  Graph<T>ret(g.size());
  for(int i=0;i<g.size();i++){
    for(auto e:g[i]){
      int to = e.to;
      e.to = i;
      ret[to].push_back(e);
    }
  }
  return ret;
}
template<typename T>
Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
  Graph<T> ret(n);
  for(int es = 0; es < m; es++){
    int u,v;
    T w=1;
    cin>>u>>v;u-=indexed,v-=indexed;
    if(weighted)cin>>w;
    ret[u].emplace_back(v,w,es);
    if(!directed)ret[v].emplace_back(u,w,es);
  }
  return ret;
}
template<typename T>
Graph<T> readParent(int n,int indexed=1,bool directed=true){
  Graph<T>ret(n);
  for(int i=1;i<n;i++){
    int p;cin>>p;
    p-=indexed;
    ret[p].emplace_back(i);
    if(!directed)ret[i].emplace_back(p);
  }
  return ret;
}
//BEGIN CUT HERE
// O(m^2 \log m \log U)
// U: maximum capacity
enum Objective{
  MINIMIZE = +1,
  MAXIMIZE = -1,
};
template<typename Flow, typename Cost,
         Objective objective = Objective::MINIMIZE>
struct MinCostFlow{
  template<typename T> inline void chmin(T &x,T y){x=min(x,y);}

  struct Edge{
    int src,dst;
    Flow flow,cap;
    Cost cost;
    int rev;
    Edge(int src,int dst,Flow cap,Cost cost,int rev):
      src(src),dst(dst),flow(0),cap(cap),cost(cost),rev(rev){}
    Flow residual_cap()const{return cap-flow;}
  };

  struct EdgePtr{
    int v,e;
    EdgePtr(int v,int e):v(v),e(e){}
  };

  int n;
  vector<vector<Edge>> G;
  vector<Flow> b;
  vector<Cost> p;

  MinCostFlow(int n):n(n),G(n),b(n,0){}

  EdgePtr add_edge(int src,int dst,Flow lower,Flow upper,Cost cost){
    int e=G[src].size();
    int r=(src==dst?e+1:G[dst].size());
    assert(lower<=upper);
    G[src].emplace_back(src,dst,+upper,+cost*objective,r);
    G[dst].emplace_back(dst,src,-lower,-cost*objective,e);
    return EdgePtr(src,e);
  }

  const Edge &get_edge(EdgePtr ep)const{return G[ep.v][ep.e];}

  void push(Edge &e,Flow amount){
    e.flow+=amount;
    G[e.dst][e.rev].flow-=amount;
  }

  void add_supply(int v,Flow amount){b[v]+=amount;}
  void add_demand(int v,Flow amount){b[v]-=amount;}

  Cost residual_cost(const Edge &e){
    return e.cost+p[e.src]-p[e.dst];
  }

  vector<int> excess_vs,deficit_vs;
  void saturate_negative(const Flow delta){
    for(auto &es:G){
      for(auto &e:es){
        Flow cap=e.residual_cap();
        cap-=cap%delta;
        if(cap<0 or residual_cost(e)<0){
          push(e,cap);
          b[e.src]-=cap;
          b[e.dst]+=cap;
        }
      }
    }

    excess_vs.clear();
    deficit_vs.clear();
    for(int v=0;v<n;v++){
      if(b[v]>0) excess_vs.emplace_back(v);
      if(b[v]<0) deficit_vs.emplace_back(v);
    }
  }

  const Cost unreachable = std::numeric_limits<Cost>::max();
  Cost farthest;
  vector<Cost> dist;
  vector<Edge*> parent;

  struct P{
    Cost first;
    int second;
    P(Cost first,int second):first(first),second(second){}
    bool operator<(const P o)const{return first>o.first;}
  };

  priority_queue<P> pq;

  template<typename Predicate>
  void eliminate(vector<int> &vs,Predicate predicate){
    vs.erase(remove_if(begin(vs),end(vs),predicate),end(vs));
  }

  bool dual(const Flow delta){
    eliminate(excess_vs, [&](int v){return b[v]<+delta;});
    eliminate(deficit_vs,[&](int v){return b[v]>-delta;});

    dist.assign(n,unreachable);
    for(int v:excess_vs) pq.emplace(dist[v]=0,v);

    parent.assign(n,nullptr);
    auto emplace=[&](Edge& e){
      if(e.residual_cap()<delta) return;
      Cost nxt=dist[e.src]+residual_cost(e);
      if(nxt>=dist[e.dst]) return;
      pq.emplace(dist[e.dst]=nxt,e.dst);
      parent[e.dst]=&e;
    };

    farthest=0;
    int deficit_count=0;
    while(!pq.empty()){
      Cost d=pq.top().first;
      int v=pq.top().second;
      pq.pop();
      if(dist[v]<d) continue;
      farthest=d;

      if(b[v]<=-delta) deficit_count++;
      if(deficit_count>=(int)deficit_vs.size()) break;

      for(auto &e:G[v]) emplace(e);
    }
    pq=decltype(pq)();

    for(int v=0;v<n;v++)
      p[v]+=min(dist[v],farthest);

    return deficit_count>0;
  }

  void primal(const Flow delta){
    for(int t:deficit_vs){
      if(dist[t]>farthest) continue;
      Flow f=-b[t];
      int v;
      for(v=t;parent[v];v=parent[v]->src)
        chmin(f,parent[v]->residual_cap());
      chmin(f,b[v]);

      f-=f%delta;
      if(f<=0) continue;

      for(v=t;parent[v];){
        auto &e=*parent[v];
        push(e,f);
        int u=parent[v]->src;
        if(e.residual_cap()<=0) parent[v]=nullptr;
        v=u;
      }
      b[t]+=f;
      b[v]-=f;
    }
  }

  template<Flow SCALING_FACTOR=2>
  bool build(){
    p.resize(n);
    Flow max_flow=1;
    for(auto t:b) max_flow=max({max_flow,t,-t});
    for(auto &es:G)
      for(auto &e:es)
        max_flow=max({max_flow,e.residual_cap(),-e.residual_cap()});

    Flow delta=1;
    while(delta<max_flow) delta*=SCALING_FACTOR;
    for(;delta;delta/=SCALING_FACTOR){
      saturate_negative(delta);
      while(dual(delta)) primal(delta);
    }

    return excess_vs.empty() and deficit_vs.empty();
  }

  template<typename T=Cost>
  T get_cost(){
    T res=0;
    for(auto &es:G)
      for(auto &e:es)
        res+=T(e.flow)*T(e.cost)/T(objective);
    return res/T(2);
  }
  template<typename T=Cost> T get_gain(){return get_cost();}

  vector<Cost> get_potential(){
    fill(p.begin(),p.end(),0);
    for(int i=0;i<n;i++)
      for(auto &es:G)
        for(auto &e:es)
          if(e.residual_cap()>0)
            chmin(p[e.dst],p[e.src]+e.cost);
    return p;
  }
};

template<typename Flow, typename Cost>
using MaxGainFlow = MinCostFlow<Flow, Cost, Objective::MAXIMIZE>;
//END CUT HERE
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
	ll n,m;cin>>n>>m;
	vector<ll>a(n);
	rep(i,0,n)cin>>a[i];
	MinCostFlow<ll,ll>mcf(n+1);
	rep(i,0,n){
		mcf.add_edge(n,i,0,1,a[i]);
		mcf.add_edge(i,n,0,1,-a[i]);
	}
	ll inf=100;
	rep(i,0,m){
		ll u,v;cin>>u>>v;u--;v--;
		mcf.add_edge(v,u,0,inf,0);
	}
	assert(mcf.build());
	auto p=mcf.get_potential();
	//cout<<mcf.get_cost()<<endl;
	vector<ll>ret(n);
	rep(i,0,n)ret[i]=(p[i]-p[n]);
	debug(ret);
  return 0;
}