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:
class Union:
  def __init__(self, num):
    self.T = [-1 for i in range(num)]

  def root(self, x):
    if self.T[x] < 0: return x
    return self.root(self.T[x])

  def size(self, x):
    return -self.T[self.root(x)]

  def merge(self, x, y):
    a = self.root(x)
    b = self.root(y)
    if a == b: return False
    if self.size(a) < self.size(b): a, b = b, a
    self.T[a] += self.T[b]
    self.T[b] = a
    return True


N, M = list(map(int, input().split()))
D = list(map(int, input().split()))
UB = [list(map(int, input().split())) for _ in range(M)]

R = {}
for i in range(M):
  a, b = UB[i]
  a -= 1
  b -= 1
  if a not in R: R[a] = [[b, i]]
  else: R[a].append([b, i])
  if b not in R: R[b] = [[a, i]]
  else: R[b].append([a, i])

DD = [[0] * 2 for _ in range(N)]
for i in range(N):
  DD[i][0] = D[i]
  DD[i][1] = i
DD.sort()
L = [0] * N
H = [0] * M
for i in range(N):
  h, x = DD[i]
  if L[x] == 0:
    for n, m in R[x]:
      if D[n] == D[x] or L[n] != 0:
        H[m] = h
        if L[n] == 1:
          L[n] = 1
          L[x] = 2
        else:
          L[n] = 2
          L[x] = 1
        break
    else:
      print(-1)
      exit()

for i in range(N):
  if L[i] == 1:
    L[i] = "B"
  else:
    L[i] = "W"
print("".join(list(map(str, L))))
for i in range(M):
  if H[i] == 0:
    print(10 ** 9)
  else:
    print(H[i])