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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline int read(){
    int x = 0; char c = getchar();
    while (!isdigit(c)) c = getchar();
    while (isdigit(c)) x = x * 10 + c - '0',c = getchar();
    return x;
}
template <typename T> void read(T &x){
	x = 0; int f = 1; char ch = getchar();
	while (!isdigit(ch)) {if (ch == '-') f = -1; ch = getchar();}
	while (isdigit(ch)) {x = x * 10 + ch - '0'; ch = getchar();}
	x *= f;
}
inline void write(int x){if (x > 9) write(x/10); putchar(x%10+'0'); }

const int N = 100050,M = 200050;
int n,m,d[N],mn[N],ex[M],ey[M],ans[M];
inline bool cmp(int x,int y){ return d[x] < d[y] || (d[x]==d[y]&&x<y); }
vector<int>G[N],G2[N],G3[N];

int To[N],col[N];
inline void solvec(int x,int c){
	if (col[x] != -1) return;
	col[x] = c;
	for (int i = 0; i < G3[x].size(); ++i) solvec(G3[x][i],c^1);
}
int main(){
	int i,j,x,y;
	n = read(),m = read();
	for (i = 1; i <= n; ++i) d[i] = read();
	for (i = 1; i <= m; ++i){
		ans[i] = 1000000000;
		ex[i] = x = read(),ey[i] = y = read();
		G[x].push_back(y),G[y].push_back(x);
		G2[x].push_back(i),G2[y].push_back(i);
	}
	int e;
	for (i = 1; i <= n; ++i){
		for (mn[i] = G[i][0],e = G2[i][0],j = 1; j < G[i].size(); ++j)
			if (cmp(G[i][j],mn[i])) mn[i] = G[i][j],e = G2[i][j];
		if (d[mn[i]] > d[i]){ puts("-1"); return 0; }
		To[i] = mn[i]; col[i] = -1;
		ans[e] = d[i];
		G3[i].push_back(To[i]),G3[To[i]].push_back(i);
	}
	for (i = 1; i <= n; ++i) if (col[i] == -1) solvec(i,0);
	for (i = 1; i <= n; ++i) putchar((col[i])?('B'):('W')); putchar('\n');
	for (i = 1; i <= m; ++i) write(ans[i]),putchar('\n');
	return 0;
}