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;

const int MAXN = 200010;

int n, m;
int a[MAXN];
vector < int > g[MAXN];
pair<int, int> edges[MAXN];

string ansS;
map<pair<int, int>, int> ansC;

int visited[MAXN];

int dfs(int v, int cost, int color) {
  ansS[v] = (color ? 'B' : 'W');
  visited[v] = 1;
  int found = 0;
  for(int s : g[v]) if(!visited[s] && a[s] == a[v]) {
    ansC[make_pair(s, v)] = ansC[make_pair(v, s)] = cost;
    dfs(s, cost, 1 - color);
    found = 1;
  }
  return found;
}

int main() {
  ios_base::sync_with_stdio(false); cin.tie(NULL);

  vector < int > p;

  cin >> n >> m;
  for(int i = 0; i < n; ++i) {
    cin >> a[i];
    p.push_back(i);
  }

  ansS = string(n, '*');

  for(int i = 0; i < m; ++i) {
    int u, v; cin >> u >> v;
    --u; --v;
    g[u].push_back(v);
    g[v].push_back(u);
    edges[i] = {u, v};
  }

  sort(p.begin(), p.end(), [&](int x, int y) {
    return a[x] < a[y];
  });

  for(int i = 0; i < n; ++i) {
    int v = p[i];
    if(visited[v]) continue;
    if(!dfs(v, a[v], 0)) {
      ansS[v] = '*';
      for(int s : g[v]) {
        if(ansS[s] != '*') {
          if(ansS[v] == '*') {
            ansS[v] = (ansS[s] == 'B' ? 'W' : 'B');
            ansC[make_pair(s, v)] = ansC[make_pair(v, s)] = a[v];
          }
          else {
            if(ansS[v] != ansS[s]) {
              ansC[make_pair(s, v)] = ansC[make_pair(v, s)] = a[v];
            }
            else {
              ansC[make_pair(s, v)] = ansC[make_pair(v, s)] = a[v] - a[s];
            }
          }
        }
      }
      if(ansS[v] == '*') return cout << -1, 0;
    }

  }

  cout << ansS << "\n";
  for(int i = 0; i < m; ++i) {
  //  cout << edges[i] << endl;
    if(!ansC.count(edges[i])) cout << (int) 1e9 << "\n";
    else cout << ansC[edges[i]] << "\n";
  }

  return 0;
}