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:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from operator import itemgetter
from collections import defaultdict

N,M = map(int,readline().split())
D = [0] + list(map(int,readline().split()))
m = map(int,read().split())
UV = list(zip(m,m))

graph = [[] for _ in range(N+1)]
for u,v in UV:
    graph[u].append((v,D[v]))
    graph[v].append((u,D[u]))

subgraph = [[] for _ in range(N+1)]
is_ng = False
for v in range(1,N+1):
    graph[v].sort(key = itemgetter(1))
    w,d = graph[v][0]
    if D[v] < d:
        is_ng = True
        break
    subgraph[w].append(v)

if is_ng:
    print(-1)
    exit()

INF = 10 ** 9
wt_edge = defaultdict(lambda:INF)
color = [0] * (N+1)

# (index, weight), sorted by wt
I = sorted(enumerate(D), key = itemgetter(1))[1:]

for v, wt in I:
    if color[v]:
        continue
    stack = [v]
    color[v] = 1
    v0 = v
    while stack:
        v = stack.pop()
        cw = 3 - color[v]
        for w in subgraph[v]:
            if w == v0:
                continue
            color[w] = cw
            wt_edge[(v,w)] = D[w]
            wt_edge[(w,v)] = D[w]
            stack.append(w)

S = ''.join('B' if x == 1 else 'W' for x in color[1:])
C = [wt_edge[(u,v)] for u,v in UV]

print(S)
print('\n'.join(map(str,C)))