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;
const int INF=1e9;

const int MAX_N=1e5+10,MAX_M=2e5+10;

int N,M,Min,w,num;
vector<int> D(MAX_N),color(MAX_N,-1),ans(MAX_M,INF);
vector<vector<pair<int,int>>> G(MAX_N);
vector<vector<int>> nG(MAX_N);

void dfs(int v,int p){
    for (int u:nG[v]){
        if (u==p) continue;
        color[u]=color[v]^1;
        dfs(u,v);
    }
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cin >> N >> M;
    for (int i=0;i<N;++i) cin >> D[i];
    for (int i=0;i<M;++i){
        int u,v; cin >> u >> v; --u,--v;
        G[u].emplace_back(v,i);
        G[v].emplace_back(u,i);
    }
    for (int v=0;v<N;++v){
        Min=INF+1;
        for (auto p:G[v]) if (D[p.first]<Min){
            Min=D[p.first]; w=p.first; num=p.second;
        }
        if (D[v]<Min){cout << -1 << '\n'; return 0;}
        ans[num]=D[v];
        nG[v].emplace_back(w);
        nG[w].emplace_back(v);
    }
    for (int v=0;v<N;++v){
        if (color[v]!=-1) continue;
        color[v]=0;
        dfs(v,-1);
    }
    for (int i=0;i<N;++i) cout << (color[i]?'B':'W');
    cout << '\n';
    for (int i=0;i<M;++i) cout << ans[i] << '\n';
}