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>
#define FOR(i, a, n) for(ll i = (ll)a; i < (ll)n; i++)
#define rep(i, n) FOR(i, 0, n)
using namespace std;
typedef long long ll;

const ll mod = 1e9 + 7;

template <class T> inline bool chmax(T &a, const T &b) {
    if(a >= b) return false;
    a = b;
    return true;
}
template <class T> inline bool chmin(T &a, const T &b) {
    if(a <= b) return false;
    a = b;
    return true;
}

/*-------------------------------------------*/

int n, m, d[100009], u[200009], v[200009];

vector<int> e[100009];

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);

    cin >> n >> m;

    vector<int> ans(m, 1e9), mn(n, 1e9 + 1), num(n);
    vector<char> c(n, '?');

    rep(i, n) cin >> d[i];
    rep(i, m) {
        cin >> u[i] >> v[i];
        u[i]--;
        v[i]--;
        if(chmin(mn[u[i]], d[v[i]])) num[u[i]] = i;
        if(chmin(mn[v[i]], d[u[i]])) num[v[i]] = i;
    }
    rep(i, n) {
        if(mn[i] > d[i]) {
            cout << -1 << endl;
            return 0;
        }
        ans[num[i]] = d[i];
        int x = (u[num[i]] == i ? v : u)[num[i]];
        e[i].push_back(x);
        e[x].push_back(i);
    }
    queue<int> que;
    rep(i, n) {
        if(c[i] == '?') {
            c[i] = 'B';
            que.push(i);
            while(!que.empty()) {
                int x = que.front();
                que.pop();
                rep(i, e[x].size()) {
                    if(c[e[x][i]] == '?') {
                        c[e[x][i]] = (c[x] == 'B' ? 'W' : 'B');
                        que.push(e[x][i]);
                    }
                }
            }
        }
        cout << c[i];
    }
    rep(i, m) cout << endl << ans[i];
}