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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
struct edge
{
  ll to;
  ll cost,num;
  edge() {}
  edge(ll to, ll cost,ll num) : to(to), cost(cost),num(num){};
};
int main()
{
ll n, m;
cin >> n >> m;
vector<vector<edge>> g(n);
vector<vector<edge>> gg(n);
vector<ll> v(n);
rep(i, n){
  cin >> v[i];
}
rep(i, m)
{
  ll a, b;
  cin >> a >> b ;
  g[a - 1].emplace_back(b - 1, -1,i);
  g[b - 1].emplace_back(a - 1, -1,i);
}
rep(i,n){
  bool ok=0;
  for(auto r:g[i])if(v[i]>=v[r.to])ok=1;
  if(!ok){
    cout << -1 << endl;
    return 0;
  }
}
vector<bool> s(n,0);
vector<bool> see(n,0);
vector<ll> ans(m,1000000000);
rep(i,n){
  if(see[i])continue;
  ll mi=1LL<<40;
  for(auto r:g[i])mi=min(mi,v[r.to]);
  for(auto r:g[i])if(mi==v[r.to]){
    ans[r.num]=v[i];
    gg[r.to].emplace_back(i, -1,i);
    gg[i].emplace_back(r.to, -1,i);
    break;}
}
rep(i,n){
  if(see[i])continue;
  queue<ll> q;
  q.push(i);
  while(!q.empty()){
    ll p=q.front();
    see[p]=1;
    q.pop();
    for(auto r:gg[p]){
      if(!see[r.to]){
        s[r.to]=!s[p];
        q.push(r.to);
      }
    }
  }
}
string ss="";
rep(i,n){
  if(s[i])ss+='B';
  else ss+='W';
}
cout << ss << endl;
for(auto r:ans)cout << r << endl;
return 0;
}