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 pi 3.1415926535897932384626
using namespace std;
      
struct P{
  int x,y;
  bool operator < (const P &a )const{
    //if(y!=a.y)
    return y>a.y;
  };
};

int a,b,c,d,i,k,n,m,e,dx[10]={1,0,-1,0,1,1,-1,-1},dy[10]={0,1,0,-1,1,-1,1,-1};
int o[100031];
int l[200055];
int j[100101];

long long x,y,z,mod=1000000007;
//string r;
char r[1];

P u[1];
queue<int> q;

//stack<int> s;
set<int> s;
map<int,int> p;
vector<P> v[100101];
vector<int> v1[100101];

bool as(P a,P b)
{
  return a.y<b.y;
}

void f(int n)
{
  for(int h=0;h<v1[n].size();h++)
  if(j[v1[n][h]]<0)
  {
    j[v1[n][h]]=1-j[n];
    f(v1[n][h]);
  }
}

int main()
{
  scanf("%d %d",&a,&b);
  c=mod;
  for(int t=1;t<=a;t++)
  {
    scanf("%d",&o[t]);
    c=min(o[t],c);
    if(c==o[t]) e=t;
  }
  for(int t=1;t<=b;t++)
  {
    scanf("%d %d",&n,&m);
    l[t]=max(o[n],o[m]);
    v[n].push_back({m,t});
    v[m].push_back({n,t});
  }
  for(int t=1;t<=a;t++)
  {
    for(int h=0;h<v[t].size();h++)
    if(l[v[t][h].y]<=o[t])
    {
      v1[t].push_back(v[t][h].x);
      v1[v[t][h].x].push_back(t);
      goto qwe;
    }
    puts("-1");
    return 0;
    qwe:;
  }
  memset(j,-1,sizeof(j));
  
  for(int t=1;t<=a;t++)
  if(j[t]<0)
  {
    j[t]=1;
    f(t);
  }
  for(int t=1;t<=a;t++)
    if(!j[t]) printf("B");
    else printf("W");
  puts("");
  for(int t=1;t<=b;t++)
    if(l[t])
    printf("%d\n",l[t]);
    else printf("1000000000\n");
}