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
input = sys.stdin.readline
N, M = map(int, input().split())
xs = list(map(int, input().split()))
G = [set() for _ in range(N+1)]
es = []
for i in range(M):
    u, v = sorted(map(int, input().split()),key=lambda x:[xs[x-1],-x])
    G[v].add(u)
    es.append((v,u))
xs,d,cc = sorted([(x,i+1) for i, x in enumerate(xs)]),{},{}
#for i in range(N):
#    if not G[i+1]:
#        print(-1)
#        sys.exit()
for x, u in xs:
    if u in cc:
        continue
    if not G[u]:
        print(-1)
        sys.exit()
    cc[u] = 1
    for c in G[u]:
        if c in cc:
            cc[u] = 1-cc[c]
    S = [u]
    while S:
        q = S.pop()
        for c in G[q]:
            d[(q,c)] = x
            if c in cc: continue
            S.append(c)
            cc[c] = 1-cc[q]
print("".join("BW"[cc[i]] for i in range(1,N+1)))
for i in range(M):
    print(d[es[i]])