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 i64 = long long;

int main() {
    int n, m;
    scanf("%d%d", &n, &m);
    std::vector<int> ds;
    std::vector<std::pair<int, int>> vs;
    for (int i = 0; i < n; i++) {
        int d;
        scanf("%d", &d);
        ds.push_back(d);
        vs.emplace_back(d, i);
    }

    std::vector<std::vector<int>> es(n);
    std::map<std::pair<int, int>, int> eindex;
    for (int i = 0; i < m; i++) {
        int a, b;
        scanf("%d%d", &a, &b);
        --a; --b;
        es[a].push_back(b);
        es[b].push_back(a);
        eindex[std::minmax(a, b)] = i;
    }

    std::sort(vs.begin(), vs.end());

    std::vector<int> cs(n, -1), elen(m);
    for (int i = 0; i < n;) {
        int j = i, cd = vs[i].first;
        while (j < n && vs[j].first == cd) j++;

        for (int k = i; k < j; k++) {
            int v = vs[k].second;
            if (cs[v] >= 0) continue;

            for (int to : es[v]) {
                if (ds[to] == cd) {
                    elen[eindex[std::minmax(v, to)]] = cd;
                    if (cs[to] >= 0) cs[v] = !cs[to];
                    else {
                        cs[v] = 0;
                        cs[to] = 1;
                    }
                    break;
                } else if (cs[to] >= 0) {
                    cs[v] = cs[to];
                    elen[eindex[std::minmax(v, to)]] = ds[v] - ds[to];
                    break;
                }
            }

            if (cs[v] == -1) {
                std::cout << -1 << std::endl;
                return 0;
            }
        }
        i = j;
    }

    for (int i = 0; i < n; i++) printf("%c", cs[i] ? 'B' : 'W');
    printf("\n");
    for (int i = 0; i < m; i++) printf("%d\n", elen[i] ? elen[i] : 1000000000);

    return 0;
}