Bichromization

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

inputFormat

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

outputFormat

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

样例

5 5
3 4 3 5 7
1 2
1 3
3 2
4 2
4 5

BWWBB
4
3
1
5
2

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