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;
#define m_p make_pair
const int N = 200005, INF = 1000000000;

int n, m;
int d[N];
vector<pair<int, int> > a[N];

char c[N];
int ans[N];

void dfs(int x)
{
    for (int i = 0; i < a[x].size(); ++i)
    {
        int h = a[x][i].first;
        if (!c[h])
        {
            if (d[h] > d[x])
            {
                c[h] = c[x];
                ans[a[x][i].second] = d[h] - d[x];
                dfs(h);
            }
        }
    }
}

int main()
{
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; ++i)
        scanf("%d", &d[i]);
    for (int i = 0; i < m; ++i)
    {
        int x, y;
        scanf("%d%d", &x, &y);
        a[x].push_back(m_p(y, i));
        a[y].push_back(m_p(x, i));
        ans[i] = INF;
        if (d[x] == d[y])
        {
            if (!c[x] && !c[y])
            {
                c[x] = 'W';
                c[y] = 'B';
                ans[i] = d[x];
            }
            else if (!c[y])
            {
                if (c[x] == 'W')
                    c[y] = 'B';
                else
                    c[y] = 'W';
                ans[i] = d[x];
            }
            else if (!c[x])
            {
                if (c[y] == 'W')
                    c[x] = 'B';
                else
                    c[x] = 'W';
                ans[i] = d[x];
            }
        }
    }
    for (int i = 1; i <= n; ++i)
    {
        if (c[i])
            dfs(i);
    }
    for (int i = 1; i <= n; ++i)
    {
        if (!c[i])
        {
            printf("-1\n");
            return 0;
        }
    }
    for (int i = 1; i <= n; ++i)
        printf("%c", c[i]);
    printf("\n");
    for (int i = 0; i < m; ++i)
        printf("%d\n", ans[i]);
    return 0;
}