p02799 Keyence Programming Contest 2020 - Bichromization
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
```python
"""
明らかに無理→最小が2つ無い or 最小同士がペアになってない
(最小から接続する頂点に最小がない)

満たしてる→最小の辺を置いちゃおう
小さい奴からGreedyに置いてく？

自分の周りにendしてるやつ or 大きさが同じやつがあったら繋げちゃう
そのとき白黒はどうでも良さそう？

"""
import sys

N,M = map(int,input().split())

D = list(map(int,input().split()))

dic2 = [[] for i in range(N)]

for i in range(M):

    U,V = map(int,input().split())
    U -= 1
    V -= 1

    if len(dic2[U]) == 0 or dic2[U][0][0] > D[V]:
        dic2[U] = []
        dic2[U].append([D[V],V,i])
    if len(dic2[V]) == 0 or dic2[V][0][0] > D[U]:
        dic2[V] = []
        dic2[V].append([D[U],U,i])


dic = [[] for i in range(N)]
for i in range(N):
    for j in dic2[i]:
        dic[i].append([j[1],j[2]])

#print (dic)

end = [False] * N
color = [0] * N
q = []
ans = [10**9] * M

for i in range(N):
    q.append([D[i],i])
q.sort()
#print (q)

for i in range(N):
    if end[q[i][1]]:
        continue
    flag = False
    for vi in dic[q[i][1]]:
        nexv = vi[0]
        mind = vi[1]
        nowd = q[i][0]
        nowp = q[i][1]
        #print (vi,q[i])

        if end[nexv]:
            flag = True
            color[nowp] = color[nexv] ^ 1
            end[nowp] = True
            ans[mind] = nowd
            break
        elif D[nexv] == nowd:
            
            flag = True
            color[nowp] = color[nexv] ^ 1
            end[nowp] = True
            end[nexv] = True
            ans[mind] = nowd
            break
        break
    #print (ans)

    if not flag:
        print (-1)
        sys.exit()


S = []
for i in color:
    if i == 0:
        S.append("B")
    else:
        S.append("W")

print ("".join(S))

print (" ".join(map(str,ans)))
        
```