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:
// ※※※ 解答不能 ※※※
// I9992147氏.
// https://atcoder.jp/contests/keyence2020/submissions/9588989
#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
using P = pair<int, int>;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)
#define pb push_back
#define a first
#define b second
#define all(x) x.begin(), x.end()
int d[202020], a[202020], b[202020], c[202020];
vi G[202020];

int main(){
    int N, M;
    map<P, int> mp;
    scanf("%d %d", &N, &M);
    repx(i, 1, N + 1) scanf("%d", &d[i]);
    repx(i, 1, M + 1){
        scanf("%d %d", &a[i], &b[i]);
        G[a[i]].pb(b[i]);
        G[b[i]].pb(a[i]);
    }
    vector<P> v;
    repx(i, 1, N + 1) v.pb({d[i], i});
    sort(all(v));
    rep(i, v.size()){
        int u = v[i].b, p = 0;
        if(c[u]) continue;
        for(auto v : G[u]){
            if(d[v] <= d[u]){
                p = v;
                break;
            }
        }
        if(!p){
            puts("-1");
            return 0;
        }
        if(!c[p]) c[p] = 1;
        c[u] = -c[p];
        mp[minmax(u, p)] = d[u];
    }
    repx(i, 1, N + 1) putchar(c[i] == 1 ? 'B' : 'W');
    puts("");
    repx(i, 1, M + 1) printf("%d\n", mp.count(minmax(a[i], b[i])) ? mp[minmax(a[i], b[i])] : 1000000000);
    return 0;
}