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<ll,ll> P;
typedef tuple<ll,ll,ll> PP;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,k,n) for(ll i=k;i<(ll)(n);i++)
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(v) v.begin(),v.end()
const ll inf=1001001001001001;
const int mod=998244353;
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<endl;}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<endl;}
template<class T> void outvv(T v){rep(i,v.size())outv(v[i]);}

int main(){
    ll n,m;cin>>n>>m;
    vi v(n);
    rep(i,n)cin>>v[i];
    vector<vector<P>> g(n);
    vector<P> hen(m);
    vi ans(m,1000000000);
    vi c(n);
    rep(i,m){
        ll a,b;cin>>a>>b;a--;b--;
        hen[i].fi=a;hen[i].se=b;
        g[a].eb(b,i);
        g[b].eb(a,i);
        if(v[a]!=v[b]||(c[a]&&c[b]))continue;
        ans[i]=v[a];
        if(c[a])c[b]=3-c[a];
        else if(c[b])c[a]=3-c[b];
        else{
            c[a]=1;c[b]=2;
        }
    }
    vector<P> s(n);
    rep(i,n)s[i].fi=v[i];
    rep(i,n)s[i].se=i;
    sort(all(s));
    rep(i,n){
        if(c[s[i].se])continue;
        for(auto ne:g[s[i].se]){
            if(v[ne.fi]>s[i].fi)continue;
            c[s[i].se]=3-c[ne.fi];
            ans[ne.se]=s[i].fi;
            break;
        }
        if(!c[s[i].se]){
            out(-1);
            return 0;
        }
    }
    rep(i,n){
        if(c[i]==1)cout<<'B';
        else cout<<'W';
    }
    cout<<endl;
    rep(i,m)cout<<ans[i]<<endl;
}