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:
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

//template
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(a);i>(b);i--)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
void tostr(ll x,string& res){while(x)res+=('0'+(x%10)),x/=10; reverse(ALL(res)); return;}
template<class T> inline bool chmax(T& a,T b){ if(a<b){a=b;return 1;}return 0; }
template<class T> inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; }
//template end

typedef pair<int,int> P;
vector<P> g[100010];
int d[100010];

int main(){
   int n,m; scanf("%d%d",&n,&m);
   rep(i,0,n)scanf("%d",&d[i]);
   rep(i,0,m){
      int u,v; scanf("%d%d",&u,&v);
      u--; v--;
      g[u].push_back({v,i});
      g[v].push_back({u,i});
   }
   map<int,vector<int>> mp;
   rep(i,0,n)mp[d[i]].push_back(i);
   vector<int> col(n,-1),res(m,1e9);
   for(auto p:mp){
      int val=p.first; vector<int> vs=p.second;
      for(auto v:vs)if(col[v]==-1){
         bool f=1;
         for(auto e:g[v]){
            int nxt=e.first;
            if(d[v]<d[nxt])continue;
            f=0; res[e.second]=val;
            if(col[nxt]==-1){
               col[v]=0; col[nxt]=1;
            }
            else col[v]=col[nxt]^1;
            break;
         }
         if(f){
            printf("-1\n");
            return 0;
         }
      }
   }
   rep(i,0,n)printf(col[i]==0?"W":"B"); puts("");
   rep(i,0,m)printf("%d\n",res[i]);
   return 0;
}