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
readline = sys.stdin.readline
from collections import Counter

N, M = map(int, readline().split())
D = list(map(int, readline().split()))
Edge = [[] for _ in range(N)]
Edgenum = Counter()
for i in range(M):
    u, v = map(int, readline().split())
    u -= 1
    v -= 1
    Edge[u].append((D[v], i, v))
    Edge[v].append((D[u], i, u))
    Edgenum[(u, v)] = i
    Edgenum[(v, u)] = i

inf = 10**9+7
table = [inf]*M

Col = [None]*N
def solve():
    Di = sorted([(D[i], i) for i in range(N)])
    for dvn, vn in Di:
        dvf, enum, vf = min(Edge[vn])
        if dvn < dvf:
            return False
        table[enum] = dvn
    
    used = set()
    for i in range(N):
        if i in used:
            continue
        Col[i] = 1
        stack = [i]
        while stack:
            vn = stack.pop()
            for _, enum, vf in Edge[vn]:
                if table[enum] == inf:
                    continue
                if vf in used:
                    continue
                Col[vf] = not Col[vn]
                used.add(vf)
                stack.append(vf)
    for i in range(M):
        if table[i] == inf:
            table[i] = 10**9
    return True

if not solve():
    print(-1)
else:
    print(''.join(['B' if Col[i] else 'W' for i in range(N)]))
    print('\n'.join(map(str, table)))