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 range(i, m, n) for(int i = m; i < n; i++)
#define husk(i, m, n) for(int i = m; i > n; i--)

int n, m;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  vector<pair<int, int>> edges;
  vector<vector<int>> g(n);
  vector<int> a(n);
  range(i, 0, n) {
    cin >> a[i];
  }
  range(i, 0, m) {
    int u, v;
    cin >> u >> v;
    u--; v--;
    g[u].push_back(v);
    g[v].push_back(u);
    edges.emplace_back(u, v);
  }

  vector<int> color(n, -1);

  range(i, 0, n) {
    bool ok = false;
    for(int j : g[i]) ok |= a[j] <= a[i];
    if(!ok) {
      cout << -1;
      return 0;
    }
  }

  for(auto x : edges) {
    int u = x.first;
    int v = x.second;
    if(a[u] == a[v]) {
      if(color[u] == -1 && color[v] == -1) {
        color[u] = 0;
        color[v] = 1;
      } else {
        if(color[u] == -1) color[u] = color[v] ^ 1;
        if(color[v] == -1) color[v] = color[u] ^ 1;
      }
    }
  }

  range(i, 0, n) if(color[i] == -1) color[i] = 0;

  range(i, 0, n) {
    cout << (color[i] ? 'B' : 'W');
  }
  cout << endl;
  for(auto x : edges) {
    int u = x.first, v = x.second;
    if(color[u] != color[v]) cout << max(a[u], a[v]);
    else {
      if(a[u] == a[v]) cout << 1000000000;
      else cout << abs(a[u] - a[v]);
    }
    cout << endl;
  }
  return 0;
}