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:
#pragma GCC optimize("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,tune=native")

#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <set>
#include <functional>
#include <iomanip>
#include <numeric>

using namespace std;

const int N = 2e5 + 5;

int d[N];
vector<pair<int, int>> g[N];
int color[N];
int weight[N];

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int n, m;
    cin >> n >> m;
    for (int i = 0; i < n; i++) {
        cin >> d[i];
    }
    for (int i = 0; i < m; i++) {
        int v, u;
        cin >> v >> u;
        --v;
        --u;
        g[v].emplace_back(u, i);
        g[u].emplace_back(v, i);
    }
    vector<int> kek(n);
    iota(kek.begin(), kek.end(), 0);
    sort(kek.begin(), kek.end(), [&](int a, int b) {
        return d[a] < d[b];
    });
    fill(weight, weight + m, 1e9);
    for (int i = 0; i < n; i++) {
        int v = kek[i];
        bool f = false;
        for (auto e : g[v]) {
            if ((color[v] != color[e.first] || color[v] * color[e.first] == 0) && d[e.first] <= d[v]) {
                if (color[v]) {
                    color[e.first] = 3 - color[v];
                }
                if (color[e.first]) {
                    color[v] = 3 - color[e.first];
                }
                if (!color[v]) {
                    color[v] = 1;
                    color[e.first] = 2;
                }
                weight[e.second] = d[v];
                f = true;
                break;
            }
        }
        if (!f) {
            cout << -1 << endl;
            return 0;
        }
    }
    for (int i = 0; i < n; i++) {
        cout << "BW"[color[i] == 1];
    }
    cout << '\n';
    for (int i = 0; i < m; i++) {
        cout << weight[i] << '\n';
    }
    return 0;
}