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 rep(i,l,r) for (int i=l,i##end=r;i<=i##end;++i)
#define per(i,r,l) for (int i=r,i##end=l;i>=i##end;--i)
#define pr pair<int,int>
#define mp make_pair
#define fi first
#define se second
#define pb push_back
using namespace std;
const int N=2e5+5;
pr a[N]; int d[N],ans[N]; bool vis[N],c[N];
vector< pr > G[N];
void dfs(int u){
    vis[u]=true;
    rep(i,0,G[u].size()-1){
        int v=G[u][i].fi;
        if (d[u]==d[v]){
            ans[G[u][i].se]=d[u];
            if (!vis[v]){ c[v]=!c[u]; dfs(v); }
        }
    }
}
bool complete(int u){
    rep(i,0,G[u].size()-1){
        int v=G[u][i].fi;
        if (d[v]<d[u]) ans[G[u][i].se]=1e9;
    }
}
int main(){
    int n,m; scanf("%d%d",&n,&m);
    rep(i,1,n){ scanf("%d",&d[i]); a[i]=mp(d[i],i); }
    rep(i,1,m){
        int u,v; scanf("%d%d",&u,&v);
        G[u].pb(mp(v,i)),G[v].pb(mp(u,i));
    }
    rep(i,1,n){
        bool t=false;
        rep(j,0,G[i].size()-1)
            if (d[G[i][j].fi]<=d[i]){ t=true; break; }
        if (!t){ cout<<-1<<endl; return 0; }
    }
    sort(a+1,a+1+n);
    rep(i,1,n){
        int u=a[i].se;
        if (vis[u]){ complete(u); continue; }
        bool t=false;
        rep(j,0,G[u].size()-1)
            if (d[u]==d[G[u][j].fi]){ t=true; break; }
        if (t){ dfs(u); complete(u); }
        else{
            rep(j,0,G[u].size()-1){
                int v=G[u][j].fi;
                if (d[v]<d[u]) ans[G[u][j].se]=c[v]?d[u]:d[u]-d[v];
            }
        }
    }
    rep(i,1,n) printf("%c",c[i]?'W':'B'); cout<<endl;
    rep(i,1,m) printf("%d\n",ans[i]);
    return 0;
}