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
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using llf = long double;
using pi = array<lint, 2>;
#define sz(v) ((int)(v).size())
#define all(v) (v).begin(), (v).end()
const int MAXT = 530000;

struct rectangle {
	int sx, ex, sy, ey;
};

struct event {
	int pos, s, e, dx;
};

vector<int> v;

struct seg {
	struct node {
		int minv, cnt[11], lazy;
		node operator+(const node &x) const {
			node ret;
			ret.minv = min(minv, x.minv);
			ret.lazy = 0;
			memset(ret.cnt, 0, sizeof(ret.cnt));
			for (int i = 0; i < 11; i++) {
				int d = minv - ret.minv + i;
				if (d < 11)
					ret.cnt[d] += cnt[i];
			}
			for (int i = 0; i < 11; i++) {
				int d = x.minv - ret.minv + i;
				if (d < 11)
					ret.cnt[d] += x.cnt[i];
			}
			return ret;
		}
	} tree[MAXT];
	void init(int s, int e, int p) {
		if (s == e) {
			tree[p].minv = tree[p].lazy = 0;
			memset(tree[p].cnt, 0, sizeof(tree[p].cnt));
			tree[p].cnt[0] = v[e + 1] - v[s];
			return;
		}
		int m = (s + e) / 2;
		init(s, m, 2 * p);
		init(m + 1, e, 2 * p + 1);
		tree[p] = tree[2 * p] + tree[2 * p + 1];
	}
	void lazydown(int p) {
		for (int i = 2 * p; i < 2 * p + 2; i++) {
			tree[i].lazy += tree[p].lazy;
			tree[i].minv += tree[p].lazy;
		}
		tree[p].lazy = 0;
	}
	void add(int s, int e, int ps, int pe, int p, int v) {
		if (e < ps || pe < s)
			return;
		if (s <= ps && pe <= e) {
			tree[p].lazy += v;
			tree[p].minv += v;
			return;
		}
		lazydown(p);
		int pm = (ps + pe) / 2;
		add(s, e, ps, pm, 2 * p, v);
		add(s, e, pm + 1, pe, 2 * p + 1, v);
		tree[p] = tree[2 * p] + tree[2 * p + 1];
	}
} seg;

vector<lint> count_small_insec(vector<rectangle> rec, int sx, int ex, int sy, int ey, int k) {
	v.clear();
	vector<lint> ret(k);
	for (auto &x : rec) {
		v.push_back(x.sy);
		v.push_back(x.ey + 1);
	}
	v.push_back(sy);
	v.push_back(ey + 1);
	sort(all(v));
	v.resize(unique(all(v)) - v.begin());
	for (auto &x : rec) {
		x.sy = lower_bound(all(v), x.sy) - v.begin();
		x.ey = lower_bound(all(v), x.ey + 1) - v.begin();
	}
	seg.init(0, sz(v) - 2, 1);
	vector<event> ev;
	ev.push_back({sx, 0, sz(v) - 1, +0});
	ev.push_back({ex + 1, 0, sz(v) - 1, +0});
	for (auto &x : rec) {
		ev.push_back({x.sx, x.sy, x.ey, +1});
		ev.push_back({x.ex + 1, x.sy, x.ey, -1});
	}
	sort(all(ev), [&](event &a, event &b) { return a.pos < b.pos; });
	for (int i = 0; i < sz(ev);) {
		int j = i;
		while (j < sz(ev) && ev[j].pos == ev[i].pos)
			j++;
		for (int k = i; k < j; k++) {
			seg.add(ev[k].s, ev[k].e - 1, 0, sz(v) - 2, 1, ev[k].dx);
		}

		if (j < sz(ev)) {
			lint d = ev[j].pos - ev[i].pos;
			for (int x = 0; x + seg.tree[1].minv < k; x++) {
				ret[x + seg.tree[1].minv] += seg.tree[1].cnt[x] * d;
			}
		}

		i = j;
	}

	return ret;
}
int main() {
	int n, k;
	cin >> n >> k;
	vector<vector<int>> a(2);
	for (int i = 0; i < 2; i++) {
		a[i].resize(n);
		for (auto &j : a[i])
			cin >> j;
	}
	vector<rectangle> rect;
	for (int i = 0; i < n; i++) {
		vector<array<int, 3>> v = {{a[0][i], 0, 0}, {a[1][i], 1, 0}, {a[0][(i + 1) % n], 0, 1}, {a[1][(i + 1) % n], 1, 1}, {0, -1, -1}, {2 * n + 1, -1, -1}};
		sort(all(v));
		for (int j = 1; j <= 4; j++) {
			for (int k = j; k <= 4; k++) {
				int chk[2][2] = {};
				for (int z = j; z <= k; z++) {
					chk[v[z][1]][v[z][2]] = 1;
				}
				if (chk[0][0] || chk[1][0]) {
					int valid = 1;
					if (chk[0][1] && chk[0][0])
						valid = 0;
					if (chk[1][1] && chk[1][0])
						valid = 0;
					if (valid)
						rect.push_back({v[j - 1][0] + 1, v[j][0], v[k][0], v[k + 1][0] - 1});
				}
			}
		}
	}
	auto ans = count_small_insec(rect, 1, 2 * n, 1, 2 * n, k + 1);
	ans[1] += ans[0] - 1ll * 2 * n * (2 * n - 1) / 2;
	for (int i = 1; i <= k; i++)
		cout << ans[i] << " ";
	cout << "\n";
}