#include <bits/stdc++.h> using namespace std; using ll = long long; using pii = pair<int, int>; using pll = pair<ll, ll>; using ld = long double; using vi = vector<int>; using vll = vector<ll>; using vii = vector<pii>; const int mod = 1e9 + 7; inline int sufit(const int& a, const int& b) { return (a + b - 1) / b; } struct Info { int min_len, time; Info() {} Info(int min_len_, int time_) : min_len(min_len_), time(time_) {} }; const int N = 3e5 + 10; ll ans[N + N]; ll weird_sum[N]; vi divs[N]; ll interval_count(ll min_len, ll max_len, ll m) { if (max_len < min_len) { return 0; } return ((m - min_len + 1LL) * (m - min_len + 2LL) - (m - max_len) * (m - max_len + 1LL)) / 2LL; } ll get_to_update(int beg, int end, int min_len, int b_len, int m) { ll res = (ll)(end - beg) * (interval_count(max(1, min_len), b_len, m)); res %= mod; return res; } struct Monotonic { map<int, Info> m; Monotonic(int time) { m[2] = {0, time}; } void update(int stab, Info info, int time, int b_len, int n) { if (stab == 2) { return; } // if (info.min_len == 0 && b_len == 1) { // return; // } b_len = min(b_len, n); ll to_update = get_to_update(info.time, time, info.min_len, b_len, n); // cout << "Update time!! " << stab << "\nlast update: " << info.time // << "\ncurrent time: " << time << "\nfrom " << max(1, info.min_len) // << " to " << b_len << " and m=" << n << " -> " << to_update << "\n"; // cout << "\n"; ans[stab] += to_update; ans[stab] %= mod; } void maybe_add(int stab, int min_len, int time, int b_len, int n) { /* We need to split the next stability into a new segment. */ if (!m.count(stab + 1)) { m[stab + 1] = {m[stab].min_len, time - 1}; } else if (m[stab + 1].time != time - 1) { // cout << "kazano mi\n"; update(stab + 1, m[stab + 1], time - 1, min_len - 2, n); m[stab + 1].time = time - 1; } Info info = m[stab]; m[stab].min_len++; m[stab].time = time - 1; auto it = m.find(stab); if (it != m.begin()) { it--; if (it->second.min_len == min_len) { m.erase(stab); } b_len = it->second.min_len - 1; } update(stab, info, time - 1, b_len, n); } }; /* k is the desired stability, returns the minimal length of the other array to get this stability. */ int minimal_count(int k, const vi& a, int from, int to) { int cnt = 0; for (int i = from; i < to - 1;) { // int len = 0; int idx = i + 1; bool yes = false; while (idx < to && a[idx] > a[idx - 1]) { yes = true; idx++; } while (!yes && idx < to && a[idx] < a[idx - 1]) { idx++; } cnt += sufit(max(0, idx - i - k), k - 1); i = idx - 1; } return cnt; } int min_cnt_for_mon(int k, int n) { return sufit(max(0, n - k), k - 1); } void count_with_shorter(int n, int m, const vi& a) { for (int i = 0; i < n - 1; i++) { vi min_lens_for_stability(n + 1); /* The case of 2-element prefix can be just solved like that, all 1-element subarrays of b are good. */ ans[2] += m; ans[2] %= mod; bool incr = a[i + 1] > a[i]; int cur_mon_suffix_len = 2; Monotonic monotonic(i); /* Intervals of length 1 and 2 are considered separately */ for (int j = i + 2; j < n; j++) { // cout << ">>> " << i << " " << j << "\n"; int len = j - i + 1; vii min_lens; // int cnt_changed = 0; if ((incr && a[j] > a[j - 1]) || (!incr && a[j] < a[j - 1])) { cur_mon_suffix_len++; for (auto d : divs[cur_mon_suffix_len - 2]) { min_lens_for_stability[d + 1]++; monotonic.maybe_add(d + 1, min_lens_for_stability[d + 1], j, min(m, len - 1), m); } } else { incr = !incr; cur_mon_suffix_len = 2; } int b_len = min(m, len - 1); // cout << "Dumping monotonic\n"; for (auto p : monotonic.m) { int stab = p.first; int min_len = p.second.min_len; // cout << stab << " " << min_len << "\n"; if (p.first == 2) { ans[stab] += interval_count(max(1, min_len), b_len, m); ans[stab] %= mod; /* UNCOMMENT THIS LATER!!!!!! */ break; } } } // cout << "Last try:\n"; int b_len = min(m, n - i); for (auto p : monotonic.m) { if (p.first != 2) { monotonic.update(p.first, p.second, n - 1, b_len, m); } b_len = min(m, p.second.min_len - 1); } // cout << i << " ans: " // << "\n"; // for (int j = 1; j <= n; j++) { // cout << ans[j] << " "; // } // cout << "\n"; } } vi a, b; int n, m; int main() { ios_base::sync_with_stdio(false); cin.tie(); cin >> n >> m; a.resize(n); b.resize(m); for (int i = 0; i < n; i++) { cin >> a[i]; } for (int i = 0; i < m; i++) { cin >> b[i]; } int mx = max(m, n); for (int i = 1; i <= mx; i++) { weird_sum[i] = weird_sum[i - 1] + interval_count(mx - i + 1, mx, mx); weird_sum[i] %= mod; } for (int i = 1; i <= max(m, n); i++) { for (int j = i; j <= max(m, n); j += i) { divs[j].push_back(i); } } count_with_shorter(n, m, a); count_with_shorter(m, n, b); for (int i = 1; i <= min(n, m); i++) { ans[2] += (ll)(n - i + 1) * (m - i + 1); ans[2] %= mod; } for (int i = 1; i <= n + m; i++) { cout << ans[i] << " "; } cout << "\n"; }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 | #include <bits/stdc++.h> using namespace std; using ll = long long; using pii = pair<int, int>; using pll = pair<ll, ll>; using ld = long double; using vi = vector<int>; using vll = vector<ll>; using vii = vector<pii>; const int mod = 1e9 + 7; inline int sufit(const int& a, const int& b) { return (a + b - 1) / b; } struct Info { int min_len, time; Info() {} Info(int min_len_, int time_) : min_len(min_len_), time(time_) {} }; const int N = 3e5 + 10; ll ans[N + N]; ll weird_sum[N]; vi divs[N]; ll interval_count(ll min_len, ll max_len, ll m) { if (max_len < min_len) { return 0; } return ((m - min_len + 1LL) * (m - min_len + 2LL) - (m - max_len) * (m - max_len + 1LL)) / 2LL; } ll get_to_update(int beg, int end, int min_len, int b_len, int m) { ll res = (ll)(end - beg) * (interval_count(max(1, min_len), b_len, m)); res %= mod; return res; } struct Monotonic { map<int, Info> m; Monotonic(int time) { m[2] = {0, time}; } void update(int stab, Info info, int time, int b_len, int n) { if (stab == 2) { return; } // if (info.min_len == 0 && b_len == 1) { // return; // } b_len = min(b_len, n); ll to_update = get_to_update(info.time, time, info.min_len, b_len, n); // cout << "Update time!! " << stab << "\nlast update: " << info.time // << "\ncurrent time: " << time << "\nfrom " << max(1, info.min_len) // << " to " << b_len << " and m=" << n << " -> " << to_update << "\n"; // cout << "\n"; ans[stab] += to_update; ans[stab] %= mod; } void maybe_add(int stab, int min_len, int time, int b_len, int n) { /* We need to split the next stability into a new segment. */ if (!m.count(stab + 1)) { m[stab + 1] = {m[stab].min_len, time - 1}; } else if (m[stab + 1].time != time - 1) { // cout << "kazano mi\n"; update(stab + 1, m[stab + 1], time - 1, min_len - 2, n); m[stab + 1].time = time - 1; } Info info = m[stab]; m[stab].min_len++; m[stab].time = time - 1; auto it = m.find(stab); if (it != m.begin()) { it--; if (it->second.min_len == min_len) { m.erase(stab); } b_len = it->second.min_len - 1; } update(stab, info, time - 1, b_len, n); } }; /* k is the desired stability, returns the minimal length of the other array to get this stability. */ int minimal_count(int k, const vi& a, int from, int to) { int cnt = 0; for (int i = from; i < to - 1;) { // int len = 0; int idx = i + 1; bool yes = false; while (idx < to && a[idx] > a[idx - 1]) { yes = true; idx++; } while (!yes && idx < to && a[idx] < a[idx - 1]) { idx++; } cnt += sufit(max(0, idx - i - k), k - 1); i = idx - 1; } return cnt; } int min_cnt_for_mon(int k, int n) { return sufit(max(0, n - k), k - 1); } void count_with_shorter(int n, int m, const vi& a) { for (int i = 0; i < n - 1; i++) { vi min_lens_for_stability(n + 1); /* The case of 2-element prefix can be just solved like that, all 1-element subarrays of b are good. */ ans[2] += m; ans[2] %= mod; bool incr = a[i + 1] > a[i]; int cur_mon_suffix_len = 2; Monotonic monotonic(i); /* Intervals of length 1 and 2 are considered separately */ for (int j = i + 2; j < n; j++) { // cout << ">>> " << i << " " << j << "\n"; int len = j - i + 1; vii min_lens; // int cnt_changed = 0; if ((incr && a[j] > a[j - 1]) || (!incr && a[j] < a[j - 1])) { cur_mon_suffix_len++; for (auto d : divs[cur_mon_suffix_len - 2]) { min_lens_for_stability[d + 1]++; monotonic.maybe_add(d + 1, min_lens_for_stability[d + 1], j, min(m, len - 1), m); } } else { incr = !incr; cur_mon_suffix_len = 2; } int b_len = min(m, len - 1); // cout << "Dumping monotonic\n"; for (auto p : monotonic.m) { int stab = p.first; int min_len = p.second.min_len; // cout << stab << " " << min_len << "\n"; if (p.first == 2) { ans[stab] += interval_count(max(1, min_len), b_len, m); ans[stab] %= mod; /* UNCOMMENT THIS LATER!!!!!! */ break; } } } // cout << "Last try:\n"; int b_len = min(m, n - i); for (auto p : monotonic.m) { if (p.first != 2) { monotonic.update(p.first, p.second, n - 1, b_len, m); } b_len = min(m, p.second.min_len - 1); } // cout << i << " ans: " // << "\n"; // for (int j = 1; j <= n; j++) { // cout << ans[j] << " "; // } // cout << "\n"; } } vi a, b; int n, m; int main() { ios_base::sync_with_stdio(false); cin.tie(); cin >> n >> m; a.resize(n); b.resize(m); for (int i = 0; i < n; i++) { cin >> a[i]; } for (int i = 0; i < m; i++) { cin >> b[i]; } int mx = max(m, n); for (int i = 1; i <= mx; i++) { weird_sum[i] = weird_sum[i - 1] + interval_count(mx - i + 1, mx, mx); weird_sum[i] %= mod; } for (int i = 1; i <= max(m, n); i++) { for (int j = i; j <= max(m, n); j += i) { divs[j].push_back(i); } } count_with_shorter(n, m, a); count_with_shorter(m, n, b); for (int i = 1; i <= min(n, m); i++) { ans[2] += (ll)(n - i + 1) * (m - i + 1); ans[2] %= mod; } for (int i = 1; i <= n + m; i++) { cout << ans[i] << " "; } cout << "\n"; } |