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())
D=list(map(int,input().split()))
EDGE=[tuple(sorted(map(int,input().split()))) for i in range(M)]
DICE=dict()

for i in range(M):
    DICE[EDGE[i]]=i
    
E=[[] for i in range(N+1)]

for x,y in EDGE:
    E[x].append(y)
    E[y].append(x)

P=[(x,ind+1) for ind,x in enumerate(D)]
P.sort()
D=[0]+D

DECIDED=[""]*(N+1)
DIS=[-1]*M

for x,po in P:
    flag=0
     
    for to in E[po]:
        if DECIDED[to]!="":
            flag=1
            break

    if flag==0:
        for to in E[po]:
            if D[to]==x:
                DIS[DICE[tuple(sorted([po,to]))]]=x
                DECIDED[po]="B"
                DECIDED[to]="W"
                break
        else:
            print(-1)
            sys.exit()

    else:            
        for to in E[po]:
            if DECIDED[to]!="" and DECIDED[po]=="":
                if DECIDED[to]=="B":
                    DECIDED[po]="W"
                else:
                    DECIDED[po]="B"
                    
                DIS[DICE[tuple(sorted([po,to]))]]=x
                break

            elif DECIDED[to]!="" and DECIDED[po]==DECIDED[to]:
                if x<=D[to]:
                    continue
                    
                DIS[DICE[tuple(sorted([po,to]))]]=x-D[to]
                break

            elif DECIDED[to]!="" and DECIDED[po]!=DECIDED[to]:
                if x<=D[to]:
                    continue
                    
                DIS[DICE[tuple(sorted([po,to]))]]=x
                break
        
print("".join(DECIDED[1:]))
for d in DIS:
    if d==-1:
        print(10**9)
    else:
        print(d)