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 <cstdio>
#include <vector>
#include <algorithm>

using namespace std;

int d[100000];
int u[200000];
int v[200000];
int par[200000];
int cnt[200000];
int ans[200000];

int find(int x) {
    if (par[x] == x) {
        return x;
    } else {
        return par[x] = find(par[x]);
    }
}

void unite(int x, int y) {
    x = find(x);
    y = find(y);
    
    if (x == y) return;
    
    par[x] = y;
    cnt[y] += cnt[x];
}

int main() {
    int n, m, i;
    vector <pair <int, int>> w;
    
    scanf("%d %d", &n, &m);
    
    for (i = 0; i < n; i++) scanf("%d", &d[i]);
    
    for (i = 0; i < m; i++) {
        scanf("%d %d", &u[i], &v[i]);
        
        u[i]--;
        v[i]--;
        
        w.push_back(make_pair(max(d[u[i]], d[v[i]]), i));
    }
    
    sort(w.begin(), w.end());
    
    for (i = 0; i < n * 2; i++) {
        cnt[i] = 1;
        par[i] = i;
    }
    
    for (i = 0; i < w.size(); i++) {
        int c = w[i].first;
        int p = w[i].second;
        int x = u[p];
        int y = v[p];
        
        if (find(x) == find(y) || find(x) == find(y + n)) {
            ans[p] = 1e9;
            
            continue;
        }
        
        if (cnt[find(x)] == 1 && cnt[find(y)] == 1) {
            if (d[x] != d[y]) {
                puts("-1");
                
                return 0;
            }
        }
        
        ans[p] = c;
        
        unite(x, y + n);
        unite(x + n, y);
    }
    
    for (i = 0; i < n; i++) {
        if (find(i) == find(0)) {
            putchar('B');
        } else {
            putchar('W');
        }
    }
    puts("");
    
    for (i = 0; i < m; i++) printf("%d\n", ans[i]);
    
    return 0;
}