1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
#include <bits/stdc++.h>
using namespace std;

#define fastIO ios_base::sync_with_stdio(0); cin.tie(0)
#define dbg(...) "[" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "

#define fi first
#define se second
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define mt make_tuple

#define readRepeatInt int _t; cin >> _t; while (_t--)
#define repeat(i, x) for (int i = 0; i < (x); ++i)
#define repeatRev(i, x) for (int i = (x) - 1; i >= 0; --i)

using ll =  long long;                  using vb = vector<bool>;
// using i128 = __int128;               using vi128 = vector<i128>;
using ull = unsigned long long;         using vull = vector<ull>;
using vll = vector<ll>;                 using vvll = vector<vll>;
using vi = vector<int>;                 using vvi = vector<vi>;

using pi = pair<int, int>;              using vpi = vector<pi>;
using pll = pair<ll, ll>;               using vpll = vector<pll>;

using si = set<int>;                    using sll = set<ll>;
using usi = unordered_set<int>;         using usll = unordered_set<ll>;
using di = deque<int>;                  using dll = deque<ll>;
using mi = map<int, int>;               using mll = map<ll, ll>;
using umi = unordered_map<int, int>;    using umll = unordered_map<ll, ll>;

using vsi = vector<si>;                 using vsll = vector<sll>;
using vusi = vector<usi>;               using vusll = vector<usll>;

template<typename A, typename B> inline A& maxi(A& a, B b) {return a = max(a, A(b)); }
template<typename A, typename B> inline A& mini(A& a, B b) {return a = min(a, A(b)); }

template <typename T> struct reversion_wrapper {T& iterable; };
template <typename T> reversion_wrapper<T> reverse(T&& iterable) {return {iterable}; }
template <typename T> auto begin(reversion_wrapper<T> w) {return rbegin(w.iterable); }
template <typename T> auto end(reversion_wrapper<T> w) {return rend(w.iterable); }

template<typename Iter> inline ostream& streamByIterators(ostream &os, Iter beg, Iter end) {os << '{'; if (beg != end) {os << *beg; while (++beg != end) os << ", " << *beg; }; return os << '}'; }
template<typename T> inline ostream& operator<<(ostream &os, const vector<T> &v) {return streamByIterators(os, v.begin(), v.end()); }
template<typename T> inline ostream& operator<<(ostream &os, const deque<T> &d) {return streamByIterators(os, d.begin(), d.end()); }
template<typename T> inline ostream& operator<<(ostream &os, const set<T> &s) {return streamByIterators(os, s.begin(), s.end()); }
template<typename T, typename V> inline ostream& operator<<(ostream &os, const map<T, V> &m) {return streamByIterators(os, m.begin(), m.end()); }
template<typename T> inline ostream& operator<<(ostream &os, const unordered_set<T> &s) {return streamByIterators(os, s.begin(), s.end()); }
template<typename T, typename V> inline ostream& operator<<(ostream &os, const unordered_map<T, V> &m) {return streamByIterators(os, m.begin(), m.end()); }
template<typename T, size_t size> inline ostream& operator<<(ostream &os, const array<T, size> &a) {return streamByIterators(os, a.begin(), a.end()); }
template<typename A, typename B> inline ostream& operator<<(ostream &os, const pair<A, B> &p) {return os << '(' << p.first << ", " << p.second << ')'; }
 
template<typename T> inline istream& operator>>(istream &is, vector<T> &v) {for (T& t : v) is >> t; return is; }
template<typename T> inline istream& operator>>(istream &is, deque<T> &d) {for (T& t : d) is >> t; return is;}
template<typename T, size_t size> inline istream& operator>>(istream &is, array<T, size> &a) {for (T& t : a) is >> t; return is; }
template<typename A, typename B> inline istream& operator>>(istream &is, pair<A, B> &p) {return is >> p.first >> p.second; }

template<typename T, typename V> T constexpr myPow(T base, V exp) {T ans(1); while (exp > 0) {if (exp & 1) ans *= base; base *= base; exp >>= 1; } return ans; }
template<typename T, typename V> T constexpr myPowMod(T base, T mod, V exp) {T ans(1); while (exp > 0) {if (exp & 1) ans = (ans * base) % mod; base = (base * base) % mod; exp >>= 1; } return ans; }
template<typename T> inline constexpr T myMod(T val, T mod) {val %= mod; if (val < 0) val += mod; return val; }
// mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
// uniform_int_distribution<int> dist(1, MX);

#define pos(x) max(x, 0LL)

bool verify(vll& a, vll& b, int n, int k, ll sc, string& ans)
{
    ll mx = 0, pref = 0;
    
    repeat(i, n)
    {
        if (ans[i] == 'A') 
        {
            pref += a[i];
            --k;
        }
        else
            pref += b[i];
            
        pref = pos(pref);
        maxi(mx, pref);
    }
    
    return mx == sc && !k;
}

int32_t main()
{
    fastIO;
    
    int n, k;
    cin >> n >> k;
    vll a(n), b(n);
    cin >> a >> b;
    
    bool swp = (k > n-k);
    if (swp)
    {
        k = n-k;
        swap(a, b);
    }

    vector<vector<vector<tuple<ll, ll, int>>>> dp(n+1, vector<vector<tuple<ll, ll, int>>>(k+1));
    
    dp[1][0].emplace_back(pos(b[0]), pos(b[0]), -1);
    if (k) dp[1][1].emplace_back(pos(a[0]), pos(a[0]), 1);
    
    for (int i = 1; i < n; ++i)
    {
        const ll A = a[i], B = b[i];
        
        for (int j = 0; j <= i && j <= k; ++j)
        {
            if (!dp[i][j].size())
                continue;
            
            sort(all(dp[i][j]));
            
            int placed = 0;
            for (int l = 1; l < (int)dp[i][j].size(); ++l)
            {
                if (get<1>(dp[i][j][l]) < get<1>(dp[i][j][placed]))
                    dp[i][j][++placed] = dp[i][j][l];
            }
            
            dp[i][j].resize(placed+1);
            
            for (int l = 0; l <= placed; ++l)
            {
                auto [mt, seg, _t] = dp[i][j][l];
                
                ll segB = pos(seg + B);
                dp[i+1][j].emplace_back(max(mt, segB), segB, -l-1);
                
                if (j == k) continue;
                
                ll segA = pos(seg + A);
                dp[i+1][j+1].emplace_back(max(mt, segA), segA, l);
            }
        }
    }
    
    auto stolen = mt(ll(1e18), ll(0), 0);
    for (auto x : dp[n][k])
        mini(stolen, x);
    ll amount = get<0>(stolen);
        
    string ans(n, 'B');
    int curr = k;
    repeatRev(i, n)
    {
        int t = get<2>(stolen);
        
        if (t >= 0) 
        {
            ans[i] = 'A';
            --curr;
        }
        else
            t = -t-1;
        
        if (!i) continue;
        
        stolen = dp[i][curr][t];
    }
    
    if (swp)
    {
        k = n-k;
        swap(a, b);
        for (char& ch : ans) ch ^= 'A' ^ 'B';
    }
    
    //assert(verify(a, b, n, k, amount, ans));
    
    cout << amount << '\n' << ans;

    return 0;
}