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
N, M = map(int, input().split())
D = list(map(int, input().split()))
DI = list(zip(D, list(range(N))))
G = [[] for _ in range(N)]
for i in range(M):
    u, v = map(int, input().split())
    G[u-1].append((v-1, i))
    G[v-1].append((u-1, i))
DI.sort()
V = [-1]*N
j = 0
used = [False]*N
ans = [10**9]*M
BW = ['']*N
for j in range(N):
    d, v = DI[j]
    if used[v]:
        continue
    for nv, i in G[v]:
        if d == D[nv]:
            if BW[nv] == '':
                BW[nv] = 'B'
                BW[v] = 'W'
                ans[i] = d
                used[v] = True
                used[nv] = True
            elif BW[nv] == 'W':
                BW[v] = 'B'
                ans[i] = d
                used[v] = True
            else:
                BW[v] = 'W'
                ans[i] = d
                used[v] = True
            break
        elif used[nv]:
            if BW[nv] == 'B':
                BW[v] = 'B'
                ans[i] = d-D[nv]
                used[v] = True
            else:
                BW[v] = 'W'
                ans[i] = d-D[nv]
                used[v] = True
            break
    if not used[v]:
        print(-1)
        sys.exit()
print(*BW, sep = '')
print(*ans, sep = '\n')