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;


void solve() {
    int n,m;
    cin >> n >> m;
    vector<int> a(n);
    for (auto& x: a) {
        cin >> x;
    }
    vector<vector<pair<int,int>>> g(n);
    vector<bool> root(n);
    for (int i = 0; i < m; i++) {
        int x,y;
        cin >> x >> y;
        x--;y--;
        if (a[x] <= a[y]) g[x].emplace_back(y,i);
        if (a[y] <= a[x]) g[y].emplace_back(x,i);
        if (a[x] == a[y]) root[x] = true;
    }
    vector<int> co(n, -1);
    vector<int> cost(m, 1e9);
    function<bool(int,int)> dfs = [&](int u, int c){
        if (co[u] != -1) return false;
        co[u] = c;
        for (auto& e: g[u]) {
            int v,i;
            tie(v,i) = e;
            if (dfs(v, c^1)) {
                cost[i] = a[v];
            }
        }
        return true;
    };
    for (int i = 0; i < n; i++) {
        if (root[i] && co[i]==-1) dfs(i, 0);
    }
    for (int i = 0; i < n; i++) {
        if (co[i]==-1) {
            cout << -1; return;
        }
    }
    for (int i = 0; i < n; i++) {
        cout << (co[i]?'B':'W');
    }cout << '\n';
    for (int x:cost) cout << x << '\n';
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    solve();
    return 0;
}