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 va first
#define vb second
using namespace std;
typedef pair<int,int> pii;
typedef pair<pii,int> ppi;
using namespace std;
const int MN = 2e5+5;
int N,M,D[MN],C[MN],Q[MN],par[MN],cnt,num;
ppi E[MN];
bool ch[MN],tree[MN],col[MN];
vector<int> T[MN];

int fnd(int a)
{
    return par[a]==a ? a : par[a]=fnd(par[a]);
}

void join(int a, int b)
{
    a = fnd(a), b = fnd(b);
    par[b] = a;
}

void dfs(int s, int r)
{
    for(int e : T[s]){
        if(e==r) continue;
        col[e] = !col[s];
        dfs(e,s);
    }
}

bool cmp(ppi p, ppi q)
{
    return max(D[p.va.va],D[p.va.vb])<max(D[q.va.va],D[q.va.vb]);
}

int main()
{
    ios_base::sync_with_stdio(0),cin.tie(0);
    cin >> N >> M;
    for(int i=1; i<=N; i++){
        par[i] = i;
        cin >> D[i];
    }
    for(int i=1; i<=N; i++){
        Q[i] = 1e9+7;
    }
    for(int i=0; i<M; i++){
        cin >> E[i].va.va >> E[i].va.vb;
        E[i].vb = i;
    }
    sort(E,E+M,cmp);
    for(int i=0; i<M; i++){
        int a = E[i].va.va;
        int b = E[i].va.vb;
        if(fnd(a)!=fnd(b)){
            join(a,b);
            T[a].push_back(b);
            T[b].push_back(a);
            C[E[i].vb] = max(D[a],D[b]);
            Q[a] = min(Q[a],C[E[i].vb]);
            Q[b] = min(Q[b],C[E[i].vb]);
            tree[E[i].vb] = 1;
            cnt++;
        }
    }
    if(cnt<N-1){
        cout << -1;
        return 0;
    }
    for(int i=1; i<=N; i++){
        if(Q[i]!=D[i]){
            cout << -1;
            return 0;
        }
    }
    dfs(1,1);
    for(int i=1; i<=N; i++){
        if(col[i]) cout << 'B';
        else cout << 'W';
    }
    cout << '\n';
    for(int i=0; i<M; i++){
        if(tree[i]) cout << C[i] << '\n';
        else cout << "1000000000\n";
    }
}