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 PYTHON3):

Solution:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
INF = 10**9

n, m = map(int, input().split())
costs = [int(item) for item in input().split()]
costs_sorted = sorted([(item, i) for i, item in enumerate(costs)], reverse=True)

edge = [[] for _ in range(n)]
edge_dict = dict()
for i in range(m):
    u, v = map(int, input().split())
    u -= 1; v -= 1
    edge[u].append(v)
    edge[v].append(u)
    if u > v:
        u, v = v, u
    edge_dict[(u, v)] = i

visited = [0] * n
color = [-1] * n
costs_on_edge = [INF] * m

while costs_sorted:
    c, v = costs_sorted.pop()
    if visited[v]:
        continue
    visited[v] = True
    ok = False
    for nv in edge[v]:
        if costs[nv] <= c:
            if color[nv] == -1 and color[v] == -1:
                color[nv] = True
                color[v] = False
                visited[nv] = True
            else:
                color[v] = not color[nv]
            if nv < v:
                costs_on_edge[edge_dict[nv, v]] = c
            else:
                costs_on_edge[edge_dict[v, nv]] = c
            ok = True
            break
    # Construction Failed
    if not ok:
        print(-1)
        exit()
color_str = ""
for item in color:
    if item == 1:
        color_str += "W"
    else:
        color_str += "B"
print(color_str)
for item in costs_on_edge:
    print(item)