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 <iostream>
#include <vector>
#include <chrono>
#include <random>
#include <cassert>
#include <algorithm>

std::mt19937 rng((int) std::chrono::steady_clock::now().time_since_epoch().count());

struct Edge {
	int u, v, c, id;
	void read() {
		std::cin >> u >> v;
		c = 1e9;
		u--;v--;
	}
};

int main() {
	std::ios_base::sync_with_stdio(false); std::cin.tie(NULL);
	int n, m;
	std::cin >> n >> m;
	std::vector<int> dist(n);
	for(int i = 0; i < n; i++) {
		std::cin >> dist[i];
	}
	std::vector<int> col(n, 0);
	std::vector<Edge> edges(m);
	int c = 0;
	for(auto &e : edges) {
		e.read();
		e.id = c++;
	}
	bool got = false;
	std::sort(edges.begin(), edges.end(), [&](Edge e1, Edge e2) { return std::min(dist[e1.u], dist[e1.v]) < std::min(dist[e2.u], dist[e2.v]); });
	for(auto &e : edges) {
		int u = e.u, v = e.v;
		if(col[u] && col[v]) continue;
		if(dist[u] != dist[v]) continue;
		if(!col[u] && !col[v]) {
			col[u] = -1;
			col[v] = 1;
		} else if (!col[u]) {
			col[u] = -col[v];
		} else {
			col[v] = -col[u];
		}
		e.c = dist[u];
		got = true;
	}
	if(!got) {
		std::cout << "-1\n";
		return 0;
	}
	for(auto &e : edges) {
		int u = e.u, v = e.v;
		if(col[u] && col[v]) continue;
		if(!col[u] && !col[v]) {
			continue;
		}
		if(!col[u] && dist[u] > dist[v]) {
			col[u] = col[v];
		} else if(!col[v] && dist[v] > dist[u]) {
			col[v] = col[u];
		} else {
			continue;
		}
		e.c = abs(dist[u] - dist[v]);
	}
	std::sort(edges.begin(), edges.end(), [&](Edge e1, Edge e2) { return e1.id < e2.id; });
	for(int i = 0; i < n; i++) {
		if(!col[i]) {
			std::cout << "-1\n";
			return 0;
		}
	}
	for(int i = 0; i < n; i++) {
		std::cout << char(col[i] == 1 ? 'W' : 'B');
	}
	std::cout << '\n';
	for(auto e : edges) {
		std::cout << e.c << '\n';
	}
}