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>

int main(){
    using namespace std;
    unsigned long N, M;
    cin >> N >> M;
    vector<unsigned long> D(N);
    for(auto& i : D)cin >> i;
    vector<unsigned long> edges(M);
    vector<vector<unsigned long>> edge(N);
    for(unsigned long i{0}, u, v; i < M; ++i){
        cin >> u >> v;
        edge[--u].push_back(i);
        edge[--v].push_back(i);
        edges[i] = u ^ v;
    }
    vector<unsigned long> ans(M, 1000000000);
    vector<unsigned long> uf(2 * N + 2), sz(2 * N + 2, 1);
    iota(uf.begin(), uf.end(), 0UL);
    const auto& find = [&uf](unsigned long i) -> unsigned long {
        while(i != uf[i])i = uf[i] = uf[uf[i]];
        return i;
    };
    const auto& unite = [&uf, &sz, &find](unsigned long i, unsigned long j) -> void {
        i = find(i);
        j = find(j);
        if(i == j)return;
        if(sz[i] < sz[j])swap(i, j);
        sz[i] += sz[j];
        uf[j] = i;
    };
    const auto& con = [&uf, &find](unsigned long i, unsigned long j) -> bool {
        return find(i) == find(j);
    };
    [&]{for(unsigned long i{0}; i < N; ++i)if([&]{
        for(auto j : edge[i])if(D[i] >= D[edges[j] ^ i]){
            ans[j] = D[i];
            unite(i, (edges[j] ^ i) + N);
            unite(i + N, (edges[j] ^ i));
            return false;
        }
        return true;
    }()){puts("-1");exit(0);}}();
    for(unsigned long i{0}; i < N; ++i)if(!con(i, 2 * N + 1)){
        unite(i, 2 * N);
        unite(i + N, 2 * N + 1);
    }
    for(unsigned long i{0}; i < N; ++i)putchar(66 + 21 * con(i, 2 * N));
    cout << endl;
    for(const auto& i : ans)cout << i << endl;
    return 0;
}