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 ll = long long;
using P = pair<int, int>;

const int MAXC = 1e9;

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int n, m;
    cin >> n >> m;
    vector<int> ids(n);
    iota(ids.begin(), ids.end(), 0);

    vector<ll> d(n);
    for (int i = 0; i < n; ++i) {
        cin >> d[i];
    }
    sort(ids.begin(), ids.end(), [&](int i1, int i2){
        return d[i1] < d[i2];
    });

    if (d[ids[0]] != d[ids[1]]) {
        cout << -1 << "\n";
        return 0;
    }

    vector< vector<int> > g(n);
    vector<int> u(m), v(m);
    map<P, int> memo;
    for (int i = 0; i < m; ++i) {
        cin >> u[i] >> v[i];
        u[i]--; v[i]--;
        if (u[i] > v[i]) swap(u[i], v[i]);
        g[u[i]].push_back(v[i]);
        g[v[i]].push_back(u[i]);
    }

    vector<int> c(n, -1);
    for (int ii = 0; ii < n; ++ii) {
        int i = ids[ii];
        if (c[i] != -1) continue;

        for (int j : g[i]) {
            if (c[j] == -1) continue;
            c[i] = 1 - c[j];
            memo[minmax(i, j)] = d[i];
            break;
        }

        if (c[i] == -1) {
            for (int j : g[i]) {
                if (d[i] != d[j]) continue;
                c[i] = 0;
                c[j] = 1;
                memo[minmax(i, j)] = d[i];
                break;
            }
        }

        if (c[i] == -1) {
            cout << -1 << "\n";
            return 0;
        }
    }

    for (int i = 0; i < n; ++i) {
        cout << "BW"[c[i]];
    }
    cout << "\n";

    for (int i = 0; i < m; ++i) {
        P tar(u[i], v[i]);
        cout << (memo.find(tar) != memo.end() ? memo[tar] : MAXC) << "\n";
    }
    return 0;
}