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:
#define _USE_MATH_DEFINES
#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <cstdio>
#include <complex>
#include <numeric>
#include <string.h>
#include <random>
#include <cmath>
#define rep(i,n) for (int i = 0; i < (int)n; i++)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<pi, pi> pp;
typedef pair<ll, ll> pl;
double PI = 3.141592653589793238462643383279;
const double EPS = 1e-9;
const ll MOD = 1000000007;
//const ll MOD = 998244353;
const int inf = 1 << 30;
const ll linf = 1LL << 60;

int n, m;
ll d[100000];
vector<pi> e[100000];
string ans;
vector<int> anse;

bool cmp (const int& l, const int& r) {
    return d[l] < d[r];
}

bool cmp2 (const pi& l, const pi& r) {
    return d[l.first] < d[r.first];
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cin >> n >> m;
    rep(i,n) cin >> d[i];
    rep(i,n) ans.push_back('B');
    anse.resize(m);
    rep(i,m) anse[i] = -1;
    rep(i,m) {
        int u, v; cin >> u >> v; u--; v--;
        e[u].push_back(pi(v,i));
        e[v].push_back(pi(u,i));
    }
    rep(i,n) sort(e[i].begin(), e[i].end(), cmp2);
    vector<int> ind(n);
    vector<int> fixed(n, 0);
    rep(i,n) ind[i] = i;
    sort(ind.begin(), ind.end(), cmp);
    rep(_,n) {
        int i = ind[_];
        if (d[e[i][0].first] > d[i]) {
            puts("-1");
            return 0;
        }
        rep(j,e[i].size()) {
            int to = e[i][j].first;
            if (d[to] > d[i]) {
                break;
            }
            if (!fixed[i]) {
                if (ans[to] == 'B') ans[i] = 'W';
                else ans[i] = 'B';
                fixed[i] = true;
                fixed[to] = true;
            }
            anse[e[i][j].second] = d[i];
        }
    }
    cout<< ans << endl;
    rep(i,m) cout << anse[i] << endl;
}