Problem:
Score : 900 points

Problem Statement

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.

Sample Input 1

5 5
3 4 3 5 7
1 2
1 3
3 2
4 2
4 5

Sample Output 1

BWWBB
4
3
1
5
2

Assume that we assign the colors and integers as the sample output, and let us consider Vertex 5, for example. To travel from Vertex 5, which is assigned black, to a vertex that is assigned white with the minimum cost, we should make these moves: Vertex 5 \to Vertex 4 \to Vertex 2. The total cost of these moves is 7, which satisfies the condition. We can also verify that the condition is satisfied for other vertices.

Sample Input 2

5 7
1 2 3 4 5
1 2
1 3
1 4
2 3
2 5
3 5
4 5

Sample Output 2

-1

Sample Input 3

4 6
1 1 1 1
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output 3

BBBW
1
1
1
2
1
1

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define _CRT_SECURE_NO_WARNINGS
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i, n) for(int i=0;i<(int)(n);i++)
#define REP(i, n) for(int i=1;i<=(int)(n);i++)
#define all(V) V.begin(),V.end()
typedef long long lint;
typedef std::pair<lint, lint> P;
constexpr int INF = INT_MAX;
constexpr lint LINF = LLONG_MAX;
constexpr double eps = 1e-9;
template<class T>
class prique :std::priority_queue<T, std::vector<T>, std::greater<T>> {};

template<class T, class Alloc = std::allocator<T>>
class Vector {

	using traits = std::allocator_traits<Alloc>;

public:

	using value_type = T;
	using allocator_type = Alloc;
	using size_type = unsigned int;
	using difference_type = int;
	using reference = T&;
	using const_reference = const T&;
	using pointer = typename traits::pointer;
	using const_pointer = typename traits::const_pointer;

	class iterator {

	public:

		using difference_type = int;
		using value_type = Vector::value_type;
		using pointer = Vector::pointer;
		using reference = Vector::reference;
		using iterator_category = std::random_access_iterator_tag;

	private:

		pointer p;

	public:

		iterator()noexcept :p() {}
		iterator(const Vector& base, difference_type index) noexcept :p(base.e + index) {}
		iterator(const iterator& i) :p(i.p) {}

		iterator& operator=(const iterator& i) = default;
		iterator& operator=(iterator&& i)noexcept = default;

		iterator& operator++() {
			p++;
			return *this;
		}

		iterator operator++(int) {
			iterator res = *this;
			p++;
			return res;
		}

		iterator operator+(const difference_type& x)const {
			iterator res = *this;
			return res += x;
		}

		iterator& operator+=(const difference_type& x) {
			p += x;
			return *this;
		}

		iterator& operator--() {
			p--;
			return *this;
		}

		iterator operator--(int) {
			iterator res = *this;
			p--;
			return res;
		}

		iterator operator-(const difference_type x)const {
			iterator res = *this;
			return res -= x;
		}

		difference_type operator-(const iterator& i)const {
			return p - i.p;
		}

		iterator& operator-=(const difference_type x) {
			p -= x;
			return *this;
		}

		reference operator*()const {
			return *p;
		}

		reference operator[](const difference_type x)const {
			return *(p + x);
		}

		bool operator<(const iterator& i)const {
			return p < i.p;
		}

		bool operator<=(const iterator& i)const {
			return p <= i.p;
		}

		bool operator==(const iterator& i)const {
			return p == i.p;
		}

		bool operator>(const iterator& i)const {
			return p > i.p;
		}

		bool operator>=(const iterator& i)const {
			return p >= i.p;
		}

		bool operator!=(const iterator& i)const {
			return p != i.p;
		}

	};

	class const_iterator {

	public:

		using difference_type = int;
		using value_type = Vector::value_type;
		using pointer = const Vector::pointer;
		using reference = const Vector::reference;
		using iterator_category = std::random_access_iterator_tag;

	private:

		pointer p;

	public:

		const_iterator()noexcept :p() {}
		const_iterator(const Vector& base, difference_type index) noexcept :p(base.e + index) {}
		const_iterator(const const_iterator& i) :p(i.p) {}

		const_iterator& operator=(const const_iterator& i)noexcept = default;
		const_iterator& operator=(const_iterator&& i)noexcept = default;

		const_iterator& operator++() {
			p++;
			return *this;
		}

		const_iterator operator++(int) {
			const_iterator res = *this;
			p++;
			return res;
		}

		const_iterator operator+(const difference_type x)const {
			const_iterator res = *this;
			return res += x;
		}

		const_iterator& operator+=(const difference_type x) {
			p += x;
			return *this;
		}

		const_iterator& operator--() {
			p--;
			return *this;
		}

		const_iterator operator--(int) {
			const_iterator res = *this;
			p--;
			return res;
		}

		const_iterator operator-(const difference_type x)const {
			const_iterator res = *this;
			return res -= x;
		}

		difference_type operator-(const const_iterator& i)const {
			return p - i.p;
		}

		const_iterator& operator-=(const difference_type x) {
			p -= x;
			return *this;
		}

		reference operator*()const {
			return *p;
		}

		reference operator[](const difference_type x)const {
			return *(p + x);
		}

		bool operator<(const const_iterator& i)const {
			return p < i.p;
		}

		bool operator<=(const const_iterator& i)const {
			return p <= i.p;
		}

		bool operator==(const const_iterator& i)const {
			return p == i.p;
		}

		bool operator>(const const_iterator& i)const {
			return p > i.p;
		}

		bool operator>=(const const_iterator& i)const {
			return p >= i.p;
		}

		bool operator!=(const const_iterator& i)const {
			return p != i.p;
		}

	};

	using reverse_iterator = std::reverse_iterator<iterator>;
	using const_reverse_iterator = std::reverse_iterator<const_iterator>;

private:

	pointer e;
	size_type length = 0, cap = 1;
	Alloc alloc;

	static_assert(std::is_same<T, typename Alloc::value_type>::value, "The allocator value type is not matched the vector value type.");
	static_assert(!std::is_const<T>::value, "This library forbids containers of const elements");

public:

	Vector() :Vector(Alloc()) {}

	explicit Vector(const Alloc& a)noexcept :alloc(a) {
		e = alloc.allocate(cap);
	}

	explicit Vector(size_type n, const Alloc& a = Alloc()) :alloc(a) {
		while (cap < n)cap *= 2;
		e = alloc.allocate(cap);
		rep(i, n)emplace_back();
	}

	explicit Vector(size_type n, const_reference value, const Alloc& a = Alloc()) :alloc(a) {
		while (cap < n)cap *= 2;
		e = alloc.allocate(cap);
		rep(i, n)emplace_back(value);
	}

	template<class InputIter>
	Vector(InputIter first, InputIter last, const Alloc& a = Alloc()) :alloc(a) {
		e = alloc.allocate(cap);
		for (InputIter i = first; i != last; i++) {
			emplace_back(*i);
		}
	}

	Vector(const Vector& x, const Alloc& a = Alloc()) :alloc(a) {
		while (cap < x.length)cap *= 2;
		length = x.length;
		e = alloc.allocate(cap);
		rep(i, x.length)traits::construct(alloc, e + i, *(x.e + i));
	}

	Vector(Vector&& x, const Alloc& a = Alloc()) :alloc(a) {
		cap = x.cap;
		length = x.length;
		e = x.e;
		x.e = nullptr;
	}

	~Vector() {
		if (e != nullptr) {
			rep(i, length)traits::destroy(alloc, e + i);
			alloc.deallocate(e, cap);
		}
	}

	Vector& operator=(const Vector& x) {
		rep(i, length)traits::destroy(alloc, e + i);
		alloc.deallocate(e, cap);
		length = x.length;
		cap = 1;
		while (cap < length)cap *= 2;
		e = alloc.allocate(cap);
		rep(i, length)traits::construct(alloc, e + i, *(x.e + i));
		return *this;
	}

	Vector& operator=(Vector&& x) {
		rep(i, length)traits::destroy(alloc, e + i);
		alloc.deallocate(e, cap);
		cap = x.cap;
		length = x.length;
		e = x.e;
		x.e = nullptr;
		return *this;
	}

private:

	void extension() {
		pointer e_ = alloc.allocate(cap * 2);
		rep(i, length)traits::construct(alloc, e_ + i, *(e + i));
		rep(i, length)traits::destroy(alloc, e + i);
		alloc.deallocate(e, cap);
		e = e_;
		cap *= 2;
	}

	void extension(size_type n) {
		unsigned int r = 1;
		while (cap * r < n)r *= 2;
		if (r == 1)return;
		pointer e_ = alloc.allocate(cap * r);
		rep(i, length)traits::construct(alloc, e_ + i, *(e + i));
		rep(i, length)traits::destroy(alloc, e + i);
		alloc.deallocate(e, cap);
		e = e_;
		cap *= r;
	}

public:

	template<class InputIter>
	void assign(InputIter first, InputIter last) {
		size_type cnt = 0;
		for (InputIter i = first; i != last; i++) {
			if (cnt == cap) {
				length = std::max(length, cnt);
				extension();
			}
			traits::construct(alloc, e + cnt, *i);
			cnt++;
		}
	}

	void assign(size_type n, const_reference value) {
		extension(n);
		std::fill(e, e + n, value);
	}

	template<class... Args>
	void emplace_back(Args&&... args) {
		if (length == cap)extension();
		traits::construct(alloc, e + length, std::forward<Args>(args)...);
		length++;
	}

	void push_back(const_reference value) {
		emplace_back(value);
	}

	void push_back(T&& value) {
		emplace_back(std::move(value));
	}

	void pop_back() {
		traits::destroy(alloc, e + length);
		length--;
	}

	void reserve(size_type n) {
		extension(n);
	}

	iterator erase(iterator pos) {
		const iterator res = pos;
		iterator t = pos; t++;
		for (iterator i = pos; t != end(); i++, t++) {
			*i = std::move(*t);
		}
		pop_back();
		return res;
	}

	iterator erase(iterator first, iterator last) {
		const iterator res = first;
		typename iterator::difference_type d = last - first;
		for (iterator i = first; i + d != end(); i++) {
			*i = std::move(*(i + d));
		}
		rep(i, d)pop_back();
		return res;
	}

	void swap(Vector& x) {
		std::swap(length, x.length);
		std::swap(cap, x.cap);
		std::swap(e, x.e);
	}

	void clear() {
		while (length)pop_back();
	}

	size_type size()const {
		return length;
	}

	void resize(size_type  n, const_reference value = T()) {
		extension(n);
		while (n < length)pop_back();
		std::fill(e, e + n, value);
	}

	size_type capacity()const {
		return cap;
	}

	bool empty()const {
		return !length;
	}

	reference operator[](const size_type pos) {
		return e[pos];
	}

	pointer data() {
		return e;
	}

	reference front() {
		return *e;
	}

	reference back() {
		return *(e + length - 1);
	}

	iterator begin() noexcept {
		return iterator(*this, 0);
	}

	const_iterator begin()const noexcept {
		return const_iterator(*this, 0);
	}

	const_iterator cbegin()const noexcept {
		return const_iterator(*this, 0);
	}

	iterator rbegin()noexcept {
		return reverse_iterator(*this, 0);
	}

	const_iterator rbegin()const noexcept {
		return const_reverse_iterator(*this, 0);
	}

	const_iterator crbegin()const noexcept {
		return const_reverse_iterator(*this, 0);
	}

	iterator end() noexcept {
		return iterator(*this, length);
	}

	const_iterator end()const noexcept {
		return const_iterator(*this, length);
	}

	const_iterator cend()const noexcept {
		return const_iterator(*this, length);
	}

	iterator rend()noexcept {
		return reverse_iterator(*this, length);
	}

	const_iterator rend()const noexcept {
		return const_reverse_iterator(*this, length);
	}

	const_iterator crend()const noexcept {
		return const_reverse_iterator(*this, length);
	}

};
template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
	if (lhs < rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
	if (lhs > rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
inline lint gcd(lint a, lint b) {
	while (b) {
		lint c = a;
		a = b; b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) {
	return a / gcd(a, b) * b;
}
bool isprime(lint n) {
	if (n == 1)return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0)return false;
	}
	return true;
}
lint mypow(lint a, lint b) {
	if (!b)return 1;
	if (b & 1)return mypow(a, b - 1) * a;
	lint memo = mypow(a, b >> 1);
	return memo * memo;
}
lint modpow(lint a, lint b, lint m) {
	if (!b)return 1;
	if (b & 1)return modpow(a, b - 1, m) * a % m;
	lint memo = modpow(a, b >> 1, m);
	return memo * memo % m;
}
template<typename T>
void printArray(std::vector<T>& vec) {
	rep(i, vec.size() - 1)std::cout << vec[i] << " ";
	std::cout << vec.back() << std::endl;
}
template<typename T>
void printArray(Vector<T>& vec) {
	rep(i, vec.size() - 1)std::cout << vec[i] << " ";
	std::cout << vec.back() << std::endl;
}
template<typename T>
void printArray(T l, T r) {
	T rprev = r;
	rprev--;
	for (T i = l; i != rprev; i++) {
		std::cout << *i << " ";
	}
	std::cout << *rprev << std::endl;
}
std::string to_string(Vector<int>& vec) {
	std::string res = "[";
	rep(i, vec.size() - 1)res += std::to_string(vec[i]) + ", ";
	res += std::to_string(vec.back()) + "]";
	return res;
}
int n, m, d[100010], u[200010], v[200010], ans[200010];
Vector<std::pair<int, P>> vec[100010];
bool use[200010], used[100010], color[100010];
void dfs(int node) {
	used[node] = true;
	for (std::pair<int, P> i : vec[node]) {
		if (!used[i.second.first] && use[i.second.second]) {
			color[i.second.first] = !color[node];
			dfs(i.second.first);
		}
	}
}
int main() {
	std::cin >> n >> m;
	REP(i, n)std::cin >> d[i];
	rep(i, m) {
		std::cin >> u[i] >> v[i];
		vec[u[i]].emplace_back(d[v[i]], std::make_pair(v[i], i));
		vec[v[i]].emplace_back(d[u[i]], std::make_pair(u[i], i));
	}
	REP(i, n) {
		bool f = false;
		for (std::pair<int, P> j : vec[i]) {
			if (j.first <= d[i]) {
				f = true;
				break;
			}
		}
		if (!f) {
			std::cout << -1 << std::endl;
			return 0;
		}
	}
	Vector<P> nodes;
	REP(i, n) {
		nodes.emplace_back(d[i], i);
	}
	std::sort(all(nodes), std::greater<P>());
	std::fill(ans, ans + m, 1e9);
	rep(i, n - 1) {
		for (std::pair<int, P> j : vec[nodes[i].second]) {
			if (nodes[i].first >= j.first) {
				if (use[j.second.second])continue;
				ans[j.second.second] = nodes[i].first;
				use[j.second.second] = true;
				break;
			}
		}
	}
	dfs(1);
	REP(i, n) {
		if (color[i])std::cout << 'B';
		else std::cout << 'W';
	}
	std::cout << std::endl;
	rep(i, m)std::cout << ans[i] << std::endl;
	return 0;
}