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;
ll n,m,i,j,en,to,d[100005],dd[100005],u,v,cg[100005],cv[100005],c[100005]={0},mn,check,cost[200005],co[100005];
bool nol[100005]={0};
vector<pair<ll,ll>> vps;
vector<pair<ll,ll>> g[100005];

int main() {
    // your code goes here
    cin >> n >> m;
    for(i=1;i<=n;i++){
        cin >> dd[i];
        vps.push_back({dd[i],i});
    }
    sort(vps.begin(),vps.end());
    for(i=0;i<n;i++){
        d[i+1]=vps[i].first;
        cg[vps[i].second]=i+1;
        cv[i+1]=vps[i].second;
    }
    if(d[1]!=d[2]){
        cout << -1 << endl; return 0;
    }
    for(i=1;i<=m;i++){
        cin >> u >> v;
        u=cg[u]; v=cg[v];
        if(u>v) swap(u,v);
        if(d[u]==d[v]){
            nol[u]=true; nol[v]=true;
        } else nol[v]=true;
        g[v].push_back({u,i});
    }
    for(i=1;i<=n;i++){
        if(!nol[i]){
            cout << -1 << endl;
            return 0;
        }
        sort(g[i].begin(),g[i].end());
    }
    mn=d[1]; check=0;
    for(i=2;i<=n;i++){
        for(j=0;j<g[i].size();j++){
            to=g[i][j].first; en=g[i][j].second;
            if(c[i]==0){
                if(c[to]==0){
                    c[to]=1; c[i]=-1;
                    cost[en]=d[i];
                } else {
                    c[i]=-c[to];
                    cost[en]=d[i];
                }
            } else {
                if(c[to]==0){
                    c[to]=-c[i];
                    cost[en]=d[i];
                } else {
                    cost[en]=d[i];
                }
            }
        }
    }
    for(i=1;i<=n;i++){
        co[cv[i]]=c[i];
    }
    for(i=1;i<=n;i++){
        if(co[i]==1) cout << "W";
        else cout << "B";
    }
    cout << endl;
    for(i=1;i<=m;i++){
        cout << cost[i] << endl;
    }
    return 0;
}