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>
#include <iomanip>
using namespace std;
#define reps(i,s,n) for(int i = s; i < n; i++)
#define rep(i,n) reps(i,0,n)
#define Rreps(i,n,e) for(int i = n - 1; i >= e; --i)
#define Rrep(i,n) Rreps(i,n,0)
#define ALL(a) a.begin(), a.end()
#define fi first
#define se second
#define mp make_pair
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;

ll N,M,H,W,K,Q,A,B;
string S, T;
//const ll MOD = 998244353;
const ll MOD = (1e+9) + 7;
const ll INF = 1LL << 60;
typedef pair<ll,ll> P;

struct edge{
    int to, id;
    edge(){};
    edge(int a, int b){
        to = a;
        id = b;
    }
};

int main() {
    cin>>N>>M;
    vector<vector<edge> > G(N, vector<edge>(0));
    vec d(N), color(N, 0), ord(N), ecost(M, -1);
    rep(i,N) {
        cin>>d[i];
        ord[i] = i;
    }
    rep(i,M){
        cin>>A>>B;
        --A;
        --B;
        G[A].emplace_back(B, i);
        G[B].emplace_back(A, i);
    }
    sort(ALL(ord), [&](int x, int y){
        return d[x] < d[y];
    });
    rep(i,N){
        int v = ord[i];
        if(color[v] != 0) continue;
        bool update = false;
        for(edge e : G[v]){
            if(color[e.to] != 0){
                color[v] = - color[e.to];
                ecost[e.id] = d[v];
                update = true;
                break;
            }
        }
        if(!update){
            color[v] = 1;
            for(edge e : G[v]){
                if(d[v] == d[e.to]){
                    color[e.to] = -1;
                    ecost[e.id] = d[v];
                }
            }
        }
    }
    rep(i,N){
        bool ok = false;
        for(edge e : G[i]){
            if(color[i] == - color[e.to] && d[i] == ecost[e.id]){
                ok = true;
            }
        }
        if(!ok){
            cout<<-1<<endl;
            return 0;
        }
    }
    rep(i,N) cout<<(color[i] == 1 ? 'B' : 'W');
    cout<<endl;
    rep(i,M) cout<<(ecost[i] == -1 ? ll(1e+9) : ecost[i])<<endl;
}