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>
#define pii pair<int, int>
#define fir first
#define sec second
using namespace std;
const int MAXN = 2e5 + 7;
const int INF = 1e9;
int head[MAXN];
struct node{int v, next, val;}e[MAXN << 1];
int tot = 1, col[MAXN];
void add(int u, int v)
{
    e[++tot] = {v, head[u], INF};
    head[u] = tot;
}
pii a[MAXN];
int d[MAXN];
int main()
{
    int n, m; scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) 
    {
        scanf("%d", &d[i]);
        a[i].fir = d[i], a[i].sec = i;
        col[i] = -1;
    }
    sort(a + 1, a + 1 + n);
    for (int i = 1, u, v; i <= m; i++)
    {
        scanf("%d%d", &u, &v);
        add(u, v); add(v, u);
    }
    for (int o = 1; o <= n; o++)
    {
        int u = a[o].sec;
        if (col[u] != -1) continue;
        int eid = 0;
        for (int i = head[u]; i; i = e[i].next)
        {
            int v = e[i].v;
            if (d[v] == d[u] && col[v] == -1) {eid = i; break;} 
            if (d[v] <= d[u] && col[v] != -1) eid = i;
        }
        if (!eid) 
        {
            puts("-1");
            return 0;
        }
        int v = e[eid].v;
        e[eid].val = e[eid ^ 1].val = d[u];
        if (col[v] == -1) {col[v] = 0; col[u] = 1;}
        else col[u] = col[v] ^ 1;
    }
    for (int i = 1; i <= n; i++) putchar(col[i] ? 'B' : 'W');
    putchar('\n');
    for (int i = 2; i <= tot; i += 2) printf("%d\n", e[i].val);
    return 0;
}