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;

const int max_n = 200222, inf = 1000000000;

int n, m, d[max_n], u[max_n], v[max_n];
int w[max_n], p[max_n];
vector<int> g[max_n];
int col[max_n];

bool cmp(int a, int b) {
    return d[a] < d[b];
}

int main() {
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; ++i) {
        scanf("%d", &d[i]);
        p[i] = i;
    }
    for (int i = 0; i < m; ++i) {
        scanf("%d%d", &u[i], &v[i]);
        --u[i];
        --v[i];
        g[u[i]].push_back(i);
        g[v[i]].push_back(i);
        w[i] = inf;
    }
    sort(p, p + n, cmp);
    for (int I = 0; I < n; ++I) {
        int i = p[I];
        if (col[i]) {
            continue;
        }
        for (int num : g[i]) {
            const int to = i ^ u[num] ^ v[num];
            if (d[to] <= d[i]) {
                if (col[to]) {
                    col[i] = 3 - col[to];
                    w[num] = d[i];
                } else {
                    col[i] = 1;
                    col[to] = 2;
                    w[num] = d[i];
                }
                break;
            }
        }
        if (!col[i]) {
            puts("-1");
            return 0;
        }
    }
    for (int i = 0; i < n; ++i) {
        printf("%c", " WB"[col[i]]);
    }
    puts("");
    for (int i = 0; i < m; ++i) {
        printf("%d\n", w[i]);
    }
    return 0;
}