Problem: We have a connected undirected graph with N vertices and M edges. Edge i in this graph (1 \leq i \leq M) connects Vertex U_i and Vertex V_i bidirectionally. We are additionally given N integers D_1, D_2, ..., D_N.

Determine whether the conditions below can be satisfied by assigning a color - white or black - to each vertex and an integer weight between 1 and 10^9 (inclusive) to each edge in this graph. If the answer is yes, find one such assignment of colors and integers, too.

* There is at least one vertex assigned white and at least one vertex assigned black.
* For each vertex v (1 \leq v \leq N), the following holds.
* The minimum cost to travel from Vertex v to a vertex whose color assigned is different from that of Vertex v by traversing the edges is equal to D_v.



Here, the cost of traversing the edges is the sum of the weights of the edges traversed.

Constraints

* 2 \leq N \leq 100,000
* 1 \leq M \leq 200,000
* 1 \leq D_i \leq 10^9
* 1 \leq U_i, V_i \leq N
* The given graph is connected and has no self-loops or multiple edges.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
D_1 D_2 ... D_N
U_1 V_1
U_2 V_2
\vdots
U_M V_M


Output

If there is no assignment satisfying the conditions, print a single line containing `-1`.

If such an assignment exists, print one such assignment in the following format:


S
C_1
C_2
\vdots
C_M


Here,

* the first line should contain the string S of length N. Its i-th character (1 \leq i \leq N) should be `W` if Vertex i is assigned white and `B` if it is assigned black.
* The (i + 1)-th line (1 \leq i \leq M) should contain the integer weight C_i assigned to Edge i.

Examples

Input

5 5
3 4 3 5 7
1 2
1 3
3 2
4 2
4 5


Output

BWWBB
4
3
1
5
2


Input

5 7
1 2 3 4 5
1 2
1 3
1 4
2 3
2 5
3 5
4 5


Output

-1


Input

4 6
1 1 1 1
1 2
1 3
1 4
2 3
2 4
3 4


Output

BBBW
1
1
1
2
1
1

Solution (in CPP):

Solution:
#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#include <tuple>
#define mkp make_pair
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;

int N,M;
vector<ll> D;
vector<int> g[100010];

#define BL 1
#define WH -1

int main(){
  cin>>N>>M;
  D.resize(N);
  rep(i,N) cin>>D[i];
  map<pair<int,int>,int> mp;
  for(int i=0;i<M;i++){
    int a,b;
    cin>>a>>b;
    a--;b--;
    if(a>b) swap(a,b);
    mp[mkp(a,b)]=i;
    g[a].push_back(b);
    g[b].push_back(a);
  }

  vector<int> ans(M,0);

  vector<pair<ll,int>> v;
  rep(i,N) v.push_back(mkp(D[i],i));
  sort(v.begin(),v.end());

  vector<int> col(N,0);
  vector<int> check(N,0);// 黒頂点に対してのみ　条件を満たす接続を既に実現しているか
  for(int i=0;i<N;i++){
    int now=v[i].second;
    for(auto nex:g[now]){
        if(col[nex]==0) continue;

        int tar=D[nex];
        if(col[nex]==BL){
            if(check[nex]==0&&D[now]>D[nex]){
                cout<<-1<<endl;
                return 0;
            }
            tar=0;
            check[nex]=1;
        }
        if(D[now]==D[nex]&&col[nex]==WH) continue;// 後回し

        int a=now,b=nex;
        if(a>b) swap(a,b);
        ans[mp[mkp(a,b)]]=D[now]-tar;
        col[now]=WH;
    }

    if(col[now]==0) col[now]=BL;
    for(auto nex:g[now]){
        if(col[nex]==WH&&D[nex]==D[now]){
            int a=now,b=nex;
            if(a>b) swap(a,b);
            ans[mp[mkp(a,b)]]=D[now];
            check[now]=1;
        }
    }
  }

  for(int i=0;i<N;i++){
    if(col[i]==BL) cout<<'B';
    else cout<<'W';
  }
  cout<<endl;
  for(int i=0;i<M;i++) cout<<ans[i]<<endl;

  return 0;
}