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;

using i64 = long long;

const i64 MOD = 1e9 + 7;
const i64 INF = i64(1e18) + 7;


template <typename T>
bool chmin(T& x, T y){
    if(x > y){
        x = y;
        return true;
    }
    return false;
}

template <typename T>
bool chmax(T& x, T y){
    if(x < y){
        x = y;
        return true;
    }
    return false;
}


signed main(){
    int n, m;
    cin >> n >> m;
    vector<int> d(n);
    for(int i = 0; i < n; ++i)
        cin >> d[i];
    vector<int> u(m), v(m);
    vector<pair<int,int>> uvp;
    vector<vector<int>> edges(n);
    for(int i = 0; i < m; ++i){
        cin >> u[i] >> v[i];
        --u[i], --v[i];
        uvp.emplace_back(minmax(u[i], v[i]));
        edges[u[i]].emplace_back(v[i]);
        edges[v[i]].emplace_back(u[i]);
    }
    vector<int> col(n, -1);
    map<pair<int,int>, int> weight;

    function<void(int)> f = [&](int x){
        for(auto& y : edges[x]){
            if(col[y] != -1 || d[x] > d[y])
                continue;
            weight[minmax(x, y)] = d[y];
            col[y] = !col[x];
            f(y);
        }
    };

    for(int i = 0; i < m; ++i){
        if(d[u[i]] == d[v[i]] && col[u[i]] == -1 && col[v[i]] == -1){
            col[u[i]] = 0;
            col[v[i]] = 1;
            weight[uvp[i]] = d[u[i]];
            f(u[i]);
            f(v[i]);
        }
    }

    if(count(col.begin(), col.end(), -1)){
        cout << -1 << endl;
        return 0;
    }

    for(int i = 0; i < n; ++i)
        cout << (col[i] ? 'B' : 'W');
    cout << endl;
    for(int i = 0; i < m; ++i)
        cout << (weight[uvp[i]] == 0 ? 1000000000 : weight[uvp[i]]) << endl;
}