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;

typedef long long ll;
typedef pair<int, int> pii;

#define fi first
#define se second
#define mp make_pair
#define fastIO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);

const int N = (int)2e5 + 9;
vector<pii> T[N];
int d[N];
int c[N];
int b[N];
vector<int> R[N];

void dfs(int u){
  for(auto x : R[u]){
    if(b[x] == -1){
      b[x]=1-b[u];
      dfs(x);
    }
  }
}

int main(){
  fastIO;
  int n, m;
  cin >> n >> m;
  for(int i = 1; i <= n; i ++ ){
    cin >> d[i];
    b[i]=-1;
    c[i]=0;
  }
  int u, v;
  for(int i = 1; i <= m; i ++ ){
    cin >> u >> v;
    T[u].push_back(mp(v,i));
    T[v].push_back(mp(u,i));
  }
  int id, ed;
  for(int i = 1; i <= n; i ++ ){
    id = -1,ed=-1;
    for(auto x : T[i]){
      if(id == -1 || d[x.fi] < d[id]){
        id = x.fi;
        ed = x.se;
      }
    }
    if(d[id] > d[i]){
      cout << -1;
      return 0;
    }
    c[ed] = d[i];
    R[i].push_back(id);
    R[id].push_back(i);
  }
  for(int i = 1; i <= n; i ++ ){
    if(b[i]==-1){
      b[i]=0;
      dfs(i);
    }
  }
  for(int i = 1; i <= n; i ++ ){
    if(b[i]==0){
      cout << "W";
    }
    else{
      cout << "B";
    }
  }
  cout << "\n";
  for(int i = 1; i <= m ; i ++ ){
    if(c[i]==0) c[i]=(int)1e9;
    cout << c[i] << "\n";
  }
  return 0;
}