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;
#define mp(a, b) make_pair(a, b)
typedef pair<int, int> pii;
const int maxn = 2e5 + 10;
const int inf = 1e9;
int n, m;
int D[maxn], col[maxn];
vector<pii> E[maxn];
vector<int> G[maxn];
bool flag[maxn];
pii ed[maxn];
void dfs(int x, int fa)
{
	col[x] = col[fa] ^ 1;
	for(auto v : G[x])
		if(v != fa)
			dfs(v, x);
}
int main()
{
	scanf("%d%d", &n, &m);
	for(int i = 1; i <= n; ++i) scanf("%d", &D[i]);
	for(int i = 1; i <= m; ++i)
	{
		int u, v;
		scanf("%d%d", &u, &v);
		E[u].push_back(mp(v, i));
		E[v].push_back(mp(u, i));
		ed[i] = mp(u, v);
	}
	for(int i = 1; i <= n; ++i)
	{
		pii Min = E[i][0];
		for(int j = 1; j < E[i].size(); ++j)
		{
			pii cur = E[i][j];
			if(D[Min.first] > D[cur.first] || (D[Min.first] == D[cur.first] && Min.second > cur.second))
				Min = cur;
		}
		if(D[i] < D[Min.first])
		{
			puts("-1");
			return 0;
		}
		flag[Min.second] = 1;
	}
	for(int i = 1; i <= m; ++i)
		if(flag[i])
		{
			int u = ed[i].first, v = ed[i].second;
			G[u].push_back(v);
			G[v].push_back(u);
		}
	memset(col, -1, sizeof col);
	col[0] = 0;
	string ans;
	for(int i = 1; i <= n; ++i)
	{
		if(col[i] == -1)
			dfs(i, 0);
		ans += col[i] ? 'W' : 'B';
	}
	cout << ans << endl;
	for(int i = 1; i <= m; ++i)
		if(flag[i])
		{
			int u = ed[i].first, v = ed[i].second;
			printf("%d\n", max(D[u], D[v]));
		}
		else
			printf("%d\n", inf);
	return 0;
}