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 fail() { cout << -1 << endl; exit(0); }
int main() {
    int N, M; cin >> N >> M;
    vector<int> D(N); for (auto &d : D) cin >> d;
    vector<pair<int, int>> E(M);
    vector<int> C(M, -1);
    for (int i = 0; i < M; i++) {
        int u, v; cin >> u >> v; u--, v--;
        E[i] = make_pair(u, v);
    }
    vector<vector<pair<int, int>>> G(N);
    for (int i = 0; i < M; i++) {
        int u, v; tie(u, v) = E[i];
        G[u].emplace_back(v, i);
        G[v].emplace_back(u, i);
    }
    vector<int> done(N);
    vector<vector<int>> H(N);
    for (int i = 0; i < M; i++) {
        int u, v; tie(u, v) = E[i];
        if (D[u] == D[v] && !done[u] && !done[v]) {
            H[u].push_back(v);
            H[v].push_back(u);
            C[i] = D[u];
            done[u] = done[v] = D[u];
        }
    }
    vector<int> I(N); iota(begin(I), end(I), 0);
    sort(begin(I), end(I), [&](int i, int j) { return D[i] < D[j]; });
    for (int i : I) if (!done[i]) {
        for (auto p : G[i]) {
            int next, idx; tie(next, idx) = p;
            if (done[next] && done[next] <= D[i]) {
                H[i].push_back(next);
                H[next].push_back(i);
                C[idx] = D[i];
                done[i] = D[i];
                break;
            }
        }
        if (!done[i]) fail();
    }
    string S(N, '?');
    function<void(int, int)> recur = [&](int node, int t) {
        if (S[node] != '?') return;
        S[node] = "BW"[t];
        for (int next : H[node]) recur(next, !t);
    };
    for (int i = 0; i < N; i++) recur(i, 0);
    cout << S << '\n';
    for (auto c : C) {
        cout << (c == -1 ? (int)1e9 : c) << '\n';
    }
    return 0;
}