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 <iostream>
#include <vector>
#include <algorithm>
#include <utility>
#define pii pair<int, int>
#define piii pair<int, pii>
#define pll pair<long long, long long>
#define plll pair<long long, pll>
#define ff first
#define ss second
#define ee ss.ff
#define rr ss.ss

using namespace std;

vector<pii> gph[101010];
bool vst[101010];
bool color[101010];
int edge[202020];

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m; cin >> n >> m;
    int tar[n]; for(auto &i : tar) cin >> i;
    for(int i = 0; i < m; ++i)
    {
        int s, e; cin >> s >> e; --s; --e;
        gph[s].push_back({e, i});
        gph[e].push_back({s, i});
    }

    int ord[n]; for(int i = 0; i < n; ++i) ord[i] = i;
    sort(ord, ord + n, [&tar](int x, int y){return tar[x] < tar[y];});

    for(auto x : ord)
    {
        if(vst[x]) continue;

        for(auto y : gph[x])
        {
            if(vst[y.ff])
            {
                vst[x] = true;
                color[x] = !color[y.ff];
                edge[y.ss] = tar[x];
                break;
            }
        }

        if(vst[x]) continue;

        for(auto y : gph[x])
        {
            if(tar[x] == tar[y.ff])
            {
                vst[x] = true;
                vst[y.ff] = true;
                color[x] = true;
                color[y.ff] = false;
                edge[y.ss] = tar[x];
                break;
            }
        }

        if(vst[x]) continue;

        cout << -1;
        return 0;
    }

    for(int i = 0; i < n; ++i) cout << (color[i] ? 'B' : 'W'); cout << '\n';
    for(int i = 0; i < m; ++i) cout << (edge[i] == 0 ? (int)1e9 : edge[i]) << '\n';
    return 0;
}