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 os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7


# MOD = 998244353


def argsort(li, key=None, reverse=False):
    return [i for _, i in sorted(
        [(a, i) for i, a in enumerate(li)], key=(lambda t: key(t[0])) if key else None, reverse=reverse
    )]


N, M = list(map(int, sys.stdin.buffer.readline().split()))
D = list(map(int, sys.stdin.buffer.readline().split()))
VU = [list(map(int, sys.stdin.buffer.readline().split())) for _ in range(M)]

graph = [[] for _ in range(N)]

for i, (v, u) in enumerate(VU):
    v -= 1
    u -= 1
    graph[v].append(u)
    graph[u].append(v)

edges = {}
colors = [None] * N
for v in argsort(D):
    d = D[v]
    if colors[v] is not None:
        continue
    for u in graph[v]:
        if colors[u] is not None:
            edges[v, u] = d
            colors[v] = not colors[u]
            break
        if D[u] == d:
            edges[v, u] = d
            colors[v] = True
            colors[u] = False
            break
    if colors[u] is None:
        print(-1)
        exit()
S = ''
for c in colors:
    S += 'B' if c else 'W'
ans = []
for v, u in VU:
    v -= 1
    u -= 1
    if (v, u) in edges:
        ans.append(edges[v, u])
    elif (u, v) in edges:
        ans.append(edges[u, v])
    else:
        ans.append(10 ** 9)

print(S)
print(*ans, sep='\n')