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 <iostream>
#include <vector>
#include <map>
#include <algorithm>
using namespace std;
using pint = pair<int,int>;
using Graph = vector<vector<pint>>;
const int INF = 1000000000;

int N, M;
Graph G;
vector<int> D;

void solve() {
    map<int, vector<int>> ma;
    for (int v = 0; v < N; ++v) ma[D[v]].push_back(v);

    vector<int> color(N, -1);
    vector<int> res(M, INF);
    for (auto it : ma) {
        int val = it.first;
        auto vs = it.second;
        for (auto v : vs) {
            if (color[v] != -1) continue; // 既に処理済み
            bool exist = false;
            for (auto e : G[v]) {
                int nv = e.first;
                if (D[v] < D[nv]) continue;
                exist = true;
                res[e.second] = val;
                if (color[nv] == -1) {
                    color[v] = 0;
                    color[nv] = 1;
                }
                else color[v] = 1 - color[nv];
                break;
            }
            if (!exist) {
                cout << -1 << endl;
                return;
            }
        }
    }
    for (int i = 0; i < N; ++i) {
        if (color[i] == 0) cout << "W";
        else cout << "B";
    }
    cout << endl;
    for (int i = 0; i < M; ++i) cout << res[i] << endl;
}

int main() {
    cin >> N >> M;
    D.resize(N);
    for (int i = 0; i < N; ++i) cin >> D[i];
    G.assign(N, vector<pint>());
    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);
    }
    solve();
}