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;

typedef long long int ll;
typedef pair<ll, ll> pll;

#define FOR(i, n, m) for(ll (i)=(m);(i)<(n);++(i))
#define REP(i, n) FOR(i,n,0)
#define OF64 std::setprecision(10)

const ll MOD = 1000000007;
const ll INF = (ll) 1e9;

struct Vertex {
    vector<pll> node;
};

Vertex V[100005];
pll D[100005];
ll T[100005];
ll C[200005];
ll S[100005];

int main() {
    ll N, M;
    cin >> N >> M;
    REP(i, N) {
        cin >> D[i].first;
        D[i].second = i;
        T[i] = D[i].first;
    }
    sort(D, D + N, [](pll a, pll b) { return a.first < b.first; });
    REP(i, M) {
        ll a, b;
        cin >> a >> b;
        a--;
        b--;
        V[a].node.push_back(pll(b, i));
        V[b].node.push_back(pll(a, i));
    }

    memset(C, 0, sizeof(C));
    memset(S, -1, sizeof(S));
    REP(i, N) {
        ll c = D[i].first;
        ll v = D[i].second;

        if (S[v] >= 0)
            continue;

        bool exist = false;
        REP(j, V[v].node.size()) {
            //! すでに色付けされている or 同じ最小コストで色付けされていないものを見つける
            ll n = V[v].node[j].first;
            if (S[n] >= 0) {
                exist = true;
                C[V[v].node[j].second] = c;
                S[v] = (S[n] + 1) % 2;
                break;
            }

            if (S[n] == -1 && T[n] == c) {
                exist = true;
                C[V[v].node[j].second] = c;
                S[v] = 0;
                S[n] = 1;
                break;
            }
        }

        if (!exist) {
            cout << -1 << endl;
            return 0;
        }
    }

    REP(i, M) {
        if (C[i] == 0)
            C[i] = INF;
    }

    REP(i, N) {
        if (S[i] == 0)
            cout << "B";
        else
            cout << "W";
    }
    cout << endl;
    REP(i, M) {
        cout << C[i] << endl;
    }

    return 0;
}