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 Graph = vector<vector<int>>;
using P = pair<int, int>;
#define INF 1000000000

void ch(int &x, int &y){
    if(y < x){
        int tmp = y;
        y = x;
        x = tmp;
    }
}

int main() {
    int N, M;
    cin >> N >> M;
    vector<int>D(N+1);
    vector<P>DS(N);
    for (int i = 1; i <= N; ++i) {
        cin >> D[i];
        DS[i-1] = P(D[i], i);
    }
    sort(DS.begin(), DS.end());
    Graph graph(N+1);
    map<P, int>mp;
    vector<int>U(M);
    vector<int>V(M);
    for (int i = 0; i < M; ++i) {
        cin >> U[i] >> V[i];
        ch(U[i], V[i]);
        mp[P(U[i], V[i])] = INF;
        graph[U[i]].push_back(V[i]);
        graph[V[i]].push_back(U[i]);
    }

    vector<int>ans(N+1, 0);
    for (int i = 0; i < N; ++i) {
        int v = DS[i].second;
        int cs = DS[i].first;
        if (ans[v]) continue;
        int flag = 0;
        for (int x: graph[v]) {
            if (ans[x] != 0) {
                int t1 = v;
                int t2 = x;
                ch(t1, t2);
                mp[P(t1, t2)] = cs;
                flag = 1;
                if (ans[x] == 1) ans[v] = 2;
                else ans[v] = 1;
                break;
            }
        }
        if (flag) continue;
        for (int x: graph[v]) {
            if (D[x] == cs) {
                flag = 1;
                ans[v] = 1;
                ans[x] = 2;
                int t1 = v;
                int t2 = x;
                ch(t1, t2);
                mp[P(t1, t2)] = cs;
                break;
            }
        }
        if (flag) continue;

        cout << -1 << "\n";
        return 0;
    }

    for (int i = 1; i <= N; ++i) {
        if (ans[i] == 1) {
            cout << "W";
        } else {
            cout << "B";
        }
    }
    cout << "\n";
    for (int i = 0; i < M; ++i) {
        cout << mp[P(U[i], V[i])] << "\n";
    }
    return 0;
}