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>
#define fi first
#define se second
using namespace std;
using P = pair<long long, long long>;

struct data {
  long long u, v, c;
};

long long n, m;
string bw;
vector<data> edge;
vector<P> d;
vector<map<long long, long long>> memo;
vector<set<long long>> lst;
vector<bool> ch;
vector<long long> dnum;

bool solve();

int main() {
  cin >> n >> m;
  dnum.resize(n);
  ch.assign(n, 0);
  for(int i = 0; i < n; ++i) {
    int x;
    cin >> x;
    dnum[i] = x;
    d.push_back({x, i});
    bw += "-";
  }
  sort(d.begin(), d.end());
  memo.resize(n);
  for(int i = 0; i < m; ++i) {
    int u, v;
    cin >> u >> v;
    --u, --v;
    edge.push_back({u, v, (long long)1e9});
    memo[u][v] = i;
    memo[v][u] = i;
  }
  if(solve()) {
    cout << bw << endl;
    for(int i = 0; i < m; ++i) cout << edge[i].c << endl;
  }
  else
    cout << -1 << endl;
  return 0;
}

bool solve() {
  lst.resize(n);
  for(int i = 0; i < n;) {
    long long numd = d[i].fi, id = i;
    while(i < n && d[i].fi == numd) {
      for(auto now : memo[d[i].se])
        if(edge[now.se].c == (long long)1e9)
          lst[now.fi].insert(d[i].se);
      ++i;
    }
    for(int j = i - 1; j >= id; --j) {
      P nowd = d[j];
      if(ch[nowd.se]) continue;
      if(lst[nowd.se].size() == 0) return 0;
      int nowid = *(lst[nowd.se].begin());
      if(bw[nowid] == 'B')
        bw[nowd.se] = 'W';
      else {
        bw[nowd.se] = 'B';
        if(bw[nowid] == '-') bw[nowid] = 'W';
      }
      edge[memo[nowd.se][nowid]].c = nowd.fi;
      lst[nowid].erase(nowd.se);
      if(dnum[nowid] == numd) ch[nowid] = 1;
    }
  }
  return 1;
}