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 rep(i, n) for (int i = 0; i < (int)(n); i++)

struct Edge {
  int to, weight;
  Edge(int t, int w) :to(t), weight(w) {}
};

struct Graph {
  vector<vector<Edge>> edges;

  Graph(int N) :edges(N) {}

  void addEdge(int a, int b) { addEdge(a, b, 1); }

  void addEdge(int a, int b, int w) {
    edges[a].emplace_back(b, w);
  }
};

int main() {
  int N, M; cin >> N >> M;
  vector<pair<int, int>> Weights;
  vector<int> D(N);
  rep(i, N) {
    cin >> D[i];
    Weights.emplace_back(D[i], i);
  }

  Graph G(N);
  rep(i, M) {
    int x, y; cin >> x >> y;
    x--; y--;
    G.addEdge(x, y, i);
    G.addEdge(y, x, i);
  }

  sort(Weights.begin(), Weights.end());

  vector<int> ans(M, 1e9);
  vector<int> color(N, -1);
  rep(i, N) {
    int d = Weights[i].first, now = Weights[i].second;
    if (color[now] != -1) continue;

    for (Edge e : G.edges[now]) {
      if (color[e.to] != -1) {
        color[now] = color[e.to] ^ 1;
        ans[e.weight] = d;
        break;
      }
      else if (D[e.to] == d) {
        color[now] = 0;
        color[e.to] = 1;
        ans[e.weight] = d;
        break;
      }
    }

    if (color[now] == -1) {
      cout << -1 << endl;
      return 0;
    }
  }

  rep(i, N) {
    if (color[i]) cout << "W";
    else cout << "B";
  }
  cout << endl;
  rep(i, M) {
    cout << ans[i] << endl;
  }
}