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
from operator import itemgetter


def solve(n, m, ddd, links):
    ddi = list(enumerate(ddd))
    ddi.sort(key=itemgetter(1))
    LIMIT = 10 ** 9 + 1
    costs = [LIMIT] * m
    for v, dv in ddi:
        du, li, u = min(links[v])
        if du > dv:
            print(-1)
            return
        costs[li] = dv

    colors = [-1] * n
    for i in range(n):
        q = [(i, 0)]
        while q:
            v, color = q.pop()
            if colors[v] != -1:
                continue
            colors[v] = color
            for du, li, u in links[v]:
                if costs[li] == LIMIT:
                    continue
                q.append((u, color ^ 1))

    MAX = 10 ** 9
    costs = [MAX if cost == LIMIT else cost for cost in costs]

    print(''.join('BW'[c] for c in colors))
    print('\n'.join(map(str, costs)))


n, m = map(int, input().split())
ddd = list(map(int, input().split()))
links = [[] for _ in range(n)]
for li, line in enumerate(sys.stdin):
    u, v = map(int, line.split())
    u -= 1
    v -= 1
    links[u].append((ddd[v], li, v))
    links[v].append((ddd[u], li, u))
solve(n, m, ddd, links)