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
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines


n,m = map(int,readline().split())
d = [-1]
d += list(map(int,readline().split()))
uv = list(map(int,read().split()))

inf = 10**9
bw = ['?'] * (n+1)
edge_cost = [inf] * (m+1)

links = [dict() for _ in range(n+1)]
links_same =[[-1,-1] for _ in range(n+1)]
roots = set()
for i in range(1,m+1):
    u,v = uv[(i-1)*2 : i*2]
    if(d[u]==d[v]):
        links_same[u] = [v,i]
        links_same[v] = [u,i]
        roots.add(u)
        roots.add(v)
    elif(d[u] < d[v]):
        links[u][v] = i
    else:
        links[v][u] = i

for root in roots:
    if(bw[root] != '?'):
        continue

    stack = [root]
    root2 = links_same[root][0]
    if(bw[root2] == 'B'):
        bw[root] = 'W'
    elif(bw[root2] == 'W'):
        bw[root] = 'B'
    else:
        bw[root] = 'B'
        bw[root2] = 'W'
        stack.append(root2)
    edge_cost[links_same[root][1]] = d[root]

    while(stack):
        i = stack.pop()
        for j,e in links[i].items():
            if(bw[j] != '?'):
                continue
            bw[j] = bw[i]
            edge_cost[e] = d[j] - d[i]
            stack.append(j)

if(bw.count('?')!=1):
    print(-1)
    exit()

print(''.join(bw[1:]))
print('\n'.join(map(str,edge_cost[1:])))