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;

template<typename T>
void out(T x) { cout << x << endl; exit(0); }
#define watch(x) cout << (#x) << " is " << (x) << endl





using ll = long long;

const ll mod = 1e9+7;
const int maxn = 1e6 + 5;
const int inf = 1e9;



int a[maxn];
int n, m;
vector<pair<int,int>> g[maxn];
bool act[maxn];
int color[maxn];
int edges[maxn];

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0);  cout.tie(0);

    memset(color,-1,sizeof(color));

    
    cin>>n>>m;


    vector<pair<int,int>> nodes;
    for (int i=0; i<n; i++) {
	cin>>a[i];
	nodes.push_back({a[i],i});
    }

    sort(nodes.begin(), nodes.end());

    for (int i=0; i<m; i++) {
	int u,v; cin>>u>>v;--u;--v;
	g[u].push_back({i,v});
	g[v].push_back({i,u});
    }

    for (int i=0; i<n; i++) {
	bool ok = false;
	for (auto ed: g[i]) {
	    int to = ed.second;
	    if (a[to] <= a[i]) {
		ok = true;
		break;
	    }
	}
	if (!ok) out(-1);
    }

    for (auto node: nodes) {
	int at = node.second;
	bool done = false;
	for (auto ed: g[at]) {
	    int id = ed.first;
	    int to = ed.second;
	    if (act[to]) {
		if (a[at] == a[to]) {
		    if (color[to] == -1) {
			color[at] = 0;
			color[to] = 1;
		    } else if (color[at] == -1) {
			color[at] = 1-color[to];
		    }
		    edges[id] = a[at];
		    done = true;
		}
	    }
	}

	if (done) {
	    for (auto ed: g[at]) {
		int to = ed.second;
		int id = ed.first;
		if (act[to] && a[to] < a[at]) {
		    edges[id] = inf;
		}
	    }
	} else {
	    for (auto ed: g[at]) {
		int to = ed.second;
		int id = ed.first;
		if (act[to]) {
		    assert(a[to] < a[at]);
		    if (color[at] == -1) {
			color[at] = color[to];
			edges[id] = a[at] - a[to];
		    } else {
			edges[id] = inf;
		    }
		}
	    }
	    
	}
	
	act[at]=true;
    }

    for (int i=0; i<n; i++) {
	cout<<(color[i]?'B':'W');
    }
    cout<<endl;
    for (int i=0; i<m; i++) {
	cout<<edges[i]<<"\n";
    }
    
    
    return 0;
}