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>
typedef long long ll;
using namespace std;
const ll mod = 1000000007;
const ll mod998 = 998244353;
const ll intmax = 2147483647;
const ll llmax = 9223372036854775807;
const char sp = ' ';

struct edge {
	int to, id;
};


int N, M, D[100000], dist[200000], uf[100000], col[100000];
vector<edge>e[100000];
vector<pair<int, int>>pp;
vector<int>a[100000];

int par(int x) {
	if (uf[x] == x)return x;
	return uf[x] = par(uf[x]);
}

void uni(int x, int y) {
	x = par(x);
	y = par(y);
	uf[x] = y;
	if (col[y] == -1) {
		col[y] = col[x];
	}
}

void dfs(int x, int from) {
	for (int i : a[x]) {
		if (i == from)continue;
		col[i] = (col[x] ^ 1);
		dfs(i, x);
	}
}

int main() {
	cin >> N >> M;
	for (int i = 0; i < N; i++) {
		cin >> D[i];
		uf[i] = i;
		col[i] = -1;
	}
	for (int i = 0; i < M; i++) {
		int u, v;
		cin >> u >> v;
		u--;
		v--;
		e[u].push_back({ v,i });
		e[v].push_back({ u,i });
	}
	for (int i = 0; i < N; i++) {
		bool f = false;
		for (int j = 0; j < e[i].size(); j++) {
			if (D[e[i][j].to] < D[i]) {
				f = true;
				dist[e[i][j].id] = D[i] - D[e[i][j].to];
				uni(e[i][j].to, i);
				break;
			}
		}
		if (!f) {
			for (int j = 0; j < e[i].size(); j++) {
				if (D[e[i][j].to] == D[i]) {
					f = true;
					dist[e[i][j].id] = D[i];
					pp.push_back({ i,e[i][j].to });
					break;
				}
			}
		}
		if (!f) {
			cout << -1 << endl;
			return 0;
		}
	}
	for (auto at : pp) {
		a[par(at.first)].push_back(par(at.second));
		a[par(at.second)].push_back(par(at.first));
	}
	for (int i = 0; i < N; i++) {
		if (col[par(i)] == -1) {
			col[par(i)] = 1;
			dfs(par(i), -1);
		}
	}
	for (int i = 0; i < N; i++) {
		cout << (col[par(i)] ? 'W' : 'B');
	}
	cout << endl;
	for (int i = 0; i < M; i++) {
		if (!dist[i])dist[i] = 1000000000;
		cout << dist[i] << endl;
	}
}