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;

#define SZ(x) (int)(x.size())

using ll = long long;
using ld = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
const double eps = 1e-10;
const ll MOD = 1000000007;
const int INF = 1000000000;
const ll LINF = 1ll<<50;

template<typename T>
void printv(const vector<T>& s) {
  for(int i=0;i<(int)(s.size());++i) {
    cout << s[i];
    if(i == (int)(s.size())-1) cout << endl;
    else cout << " ";
  }
}

template<typename T1, typename T2>
ostream& operator<<(ostream &os, const pair<T1, T2> p) {
  os << p.first << ":" << p.second;
  return os;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(10);

  int n, m; cin >> n >> m;
  vll d(n);
  for(int i=0;i<n;++i) {
    cin >> d[i];
  }

  map<P, int> edges;
  vector<vector<int>> g(n);
  vector<ll> cost(m, INF);
  vector<int> col(n, -1);
  for(int i=0;i<m;++i) {
    int u, v; cin >> u >> v;
    u--; v--;
    if(u > v) swap(u, v);
    
    g[u].push_back(v);
    g[v].push_back(u);
    edges[{u, v}] = i;
  }

  map<int, vi> ma;
  for(int i=0;i<n;++i) {
    ma[d[i]].push_back(i);
  }

  for(auto it: ma) {
    int val = it.first;
    auto vs = it.second;
    for(auto v: vs) {
      if(col[v] != -1) continue;
      bool exist = false;
      for(auto e: g[v]) {
        int nv = e;
        if(d[v] < d[nv]) continue;
        exist = true;
        if(v < nv) cost[edges[{v, nv}]] = val;
        else cost[edges[{nv, v}]] = val;
        if(col[nv] == -1) {
          col[v] = 0;
          col[nv] = 1;
        }
        else col[v] = 1 - col[nv];
        break;
      }
      
      if(!exist) {
        cout << -1 << endl;
        return 0;
      }
    }
  }

  for(int i=0;i<n;++i) {
    cout << (col[i] ? 'W' : 'B');
  }
  cout << endl;
  for(int i=0;i<m;++i) {
    cout << cost[i] << endl;
  }

}