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:
from collections import defaultdict
import sys
input = sys.stdin.readline
N, M = map(int, input().split())
bxs = list(map(int, input().split()))
xs = bxs[:]
dd = defaultdict(set)
for i, x in enumerate(xs):
    dd[x].add(i+1)
xs = list(set(xs))
xs.sort()

#for x, i in xs:
G = [set() for _ in range(N+1)]
G2 = [set() for _ in range(N+1)]
es = []
for i in range(M):
    u, v = map(int, input().split())
    if bxs[u-1] == bxs[v-1]:
        G[v].add(u)
        G[u].add(v)
    elif bxs[u-1] > bxs[v-1]:
        G[u].add(v)
    else:
        G[v].add(u)
    e = (min(u,v), max(u,v))
    es.append(e)

r = True
d = dict()
cc = [-1 for _ in range(N+1)]
for i in range(N):
    if len(G[i+1]) == 0:
        print(-1)
        sys.exit()
for x in xs:
    for u in dd[x]:
        if cc[u] != -1:
            continue
        for c in G[u]:
            if cc[c] == -1:
                cc[u] = 1
                break
            else:
                cc[u] = 1-cc[c]
        stack = [u]
        while stack:
            q = stack.pop()
            for c in G[q]:
                e = (min(q,c), max(q,c))
                if e in d:
                    continue
                d[e] = x
                if cc[c] != -1:
                    continue
                stack.append(c)
                cc[c] = 1 - cc[q]
for i in range(1, N+1):
    if cc[i] == -1:
        print(-1)
        sys.exit()
for i in range(1, N+1):
    print("B"if cc[i] else "W", end="")
print()
for i in range(M):
    print(d[es[i]])