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;
#define ll long long

int main() {
    int N, M;
    cin >> N >> M;
    vector<int> D(N);
    for (int i = 0; i < N; i++) cin >> D[i];
    vector<vector<pair<int, int>>> edge(N+1);
    for (int i = 0; i < M; i++) {
        int u, v;
        cin >> u >> v;
        edge[u].push_back({v, i+1});
        edge[v].push_back({u, i+1});
    }
    vector<int> anse(M+1, 1000000000), ansv(N+1, 0);
    vector<pair<int, int>> p(N);
    for (int i = 0; i < N; i++) p[i] = {D[i], i+1};
    sort(p.begin(), p.end());
    if (p[0].first != p[1].first) {
        cout << -1 << endl;
        return 0;
    }
    for (int i = 0; i < N; i++) {
        int now = p[i].second;
        if (ansv[now] > 0) continue;
        for (auto pair : edge[now]) {
            int nxt = pair.first;
            if (ansv[nxt] > 0) {
                anse[pair.second] = p[i].first;
                ansv[now] = 3-ansv[nxt];
                break;
            }
        }
        if (ansv[now] == 0) {
            int me = edge[now][0].second, mv = edge[now][0].first;
            for (auto pair : edge[now]) {
                if (D[mv-1] > D[pair.first-1]) {
                    mv = pair.first;
                    me = pair.second;
                }
            }
            if (D[mv-1] > D[now-1]) {
                cout << -1 << endl;
                return 0;
            }
            anse[me] = D[now-1];
            ansv[now] = 1;
            ansv[mv] = 2;
        }
    }
    for (int i = 1; i <= N; i++) {
        cout << ((ansv[i] == 1) ?  'B' : 'W');
    }
    cout << endl;
    for (int i = 1; i <= M; i++) {
        cout << anse[i] << endl;
    }
    return 0;
}