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//#pragma GCC optimize("O3")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ //
namespace debug {
template <class c> struct rge { c b, e; }; template <class c> rge<c> range(c i, c j) { return rge<c>{i, j}; }
template <class c> char elo(...); template <class c> auto elo(c* a) -> decltype(cerr << *a, 0);
struct stream { ~stream() { cerr << endl; }
template <class c> typename enable_if <sizeof elo<c>(0) != 1, stream&>::type operator<<(c i) { cerr << boolalpha << i; return *this; }
template <class c> typename enable_if <sizeof elo<c>(0) == 1, stream&>::type operator<<(c i) { return *this << range(begin(i), end(i)); }
template <class a, class b> stream& operator<<(pair <a,b> p) { return *this << "(" << p.first << ", " << p.second << ")"; }
template <class c> stream& operator<<(rge<c> d) { *this << "["; for (auto it=d.b; it!=d.e; it++) *this << ", " + 2 * (it == d.b) << *it; return *this << "]"; }
stream& _dbg(const string& s, int i, int b) { return *this; } template <class c, class ... cs> stream& _dbg(const string& s, int i, int b, c arg, cs ... args) {
if (i == s.size()) return (*this << ": " << arg << ""); b += (s[i] == '(') + (s[i] == '[') + (s[i] == '{'); b -= (s[i] == ')') + (s[i] == ']') + (s[i] == '}');
if (s[i] == ',' && b == 0) return (*this << ": " << arg << "     ")._dbg(s, i+1, b, args...); return (s[i] == ' ' ? *this : *this << s[i])._dbg(s, i+1, b, arg, args...); } };}
#define dout debug::stream()
#define dbg(...) ((dout << ">> ")._dbg(#__VA_ARGS__, 0, 0, __VA_ARGS__))
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ //
#define f first
#define s second
#define sc scanf
#define pr printf
#define mp make_pair
#define pb push_back
#define all(x) x.begin(),x.end()
#define ss(x) ((int)((x).size()))
#define rep0(i, b) for(int (i)=(0);i<(b);(i)++)
#define rep1(i, b) for(int (i)=(1);i<=(b);(i)++)
#define rep(i, a, b) for(int (i)=(a);i<=(b);(i)++)
#define per(i, a, b) for(int (i)=(b);i>=(a);(i)--)
#define lowb(v, x) (lower_bound(all(v),(x))-(v).begin())
#define uppb(v, x) (upper_bound(all(v),(x))-(v).begin())
#define upgrade ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define erase_duplicates(x) {sort(all(x));(x).resize(distance((x).begin(), unique(all(x))));}
template <class p, class q> pair<p,q> operator-(pair<p,q> a, pair<p,q> b) { return mp(a.f-b.f, a.s-b.s); }
template <class p, class q> pair<p,q> operator+(pair<p,q> a, pair<p,q> b) { return mp(a.f+b.f, a.s+b.s); }
template <class p, class q> void umin(p& a, const q& b) { if (a > b) a = b; }
template <class p, class q> void umax(p& a, const q& b) { if (a < b) a = b; }
using lf=long double;
using ll=long long;
using cll=const ll;
using cint=const int;
using pll=pair<ll,ll>;
using pii=pair<int,int>;
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ //

const ll inf = 1000000000000000005;
const int N = 100005;
int n, k;
ll t[N];
ll L[N];
ll R[N];
int v[N];
int T[N][2];
int opt[N];
bool valid[N];
set < pair <int,int> > S;

int check(ll lim){
	
	rep(i, 0, n){
		if (R[i] - L[i] > lim){
			return -1;
		}
	}
	
	ll P = R[n];
	ll sum = 0;
	S.clear();
	per(j, 1, n){
		int i = j - 1;
		if (valid[j] == true){
			S.insert({v[j], j});
			sum += v[j];
		}
		while (P < R[i]){
			auto it = S.lower_bound({1, 0});
			if (it == S.end()){
				P = R[i];
				break;
			}
			auto p = *it;
			S.erase(it);
			sum -= p.f;
			if (p.f >= R[i] - P){
				p.f -= R[i] - P;
				S.insert(p);
				sum += p.f;
				P = R[i];
				break;
			}
			P += p.f;
			p.f = 0;
			S.insert(p);
			assert(P < R[i]);
		}
		while (P + sum - L[i] > lim){
			assert(S.empty() == false);
			auto it = prev(S.end());
			auto p = *it;
			S.erase(it);
			sum -= p.f;
		}
	}

	return ss(S);
}

ll verify(){
	
	rep(i, 1, n){
		t[i] = T[i][opt[i]];
		t[i] += t[i - 1];
	}

	L[0] = 0;
	rep(i, 1, n){
		L[i] = min(L[i - 1], t[i]);
	}

	R[n] = t[n];
	per(i, 0, n - 1){
		R[i] = max(R[i + 1], t[i]);
	}

	ll lim = 0;
	rep(i, 0, n){
		umax(lim, R[i] - L[i]);
	}

	return lim;
}

int main (){
	
	scanf("%d%d", &n, &k);

	rep(j, 0, 1){
		rep(i, 1, n){
			scanf("%d", &T[i][j]);
		}
	}

	int ini = 0;
	rep(i, 1, n){
		opt[i] = (T[i][0] >= T[i][1]);
		t[i] = T[i][opt[i]];
		ini += (opt[i] == 0);
	}

	rep(i, 1, n){
		if (ini <= k){
			if (opt[i] == 1){
				valid[i] = true;
				v[i] = T[i][0] - T[i][1];
			}
		}else{
			if (opt[i] == 0){
				valid[i] = true;
				v[i] = T[i][1] - T[i][0];
			}
		}
		assert(v[i] >= 0);
	}

	rep(i, 1, n){
		t[i] += t[i - 1];
	}

	L[0] = 0;
	rep(i, 1, n){
		L[i] = min(L[i - 1], t[i]);
	}

	R[n] = t[n];
	per(i, 0, n - 1){
		R[i] = max(R[i + 1], t[i]);
	}

	int dif = abs(ini - k);

	ll a = -1;
	ll b = inf;
	while (b - a > 1){
		(check((a + b) / 2) >= abs(ini - k) ? b : a) = (a + b) / 2;
	}

	void(check(b));
	
	assert(ss(S) >= dif);
	
	for (auto p : S){
		if (dif == 0){
			break;	
		}
		opt[p.s] ^= 1;
		dif -= 1;
	}

	printf("%lld\n", b);
	
	rep(i, 1, n){
		printf("%c", opt[i] == 0 ? 'A' : 'B');
	}
	
	printf("\n");

	return 0;
}