## solution

$N \le 10^{13}$と大きい。クエリを先読みして座標圧縮し、配列の要素には長さの属性を持たせる。

$10^{18}+9$での剰余を忘れないように。

## implementation

#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
#include <array>
#include <map>
#include <functional>
#include <cmath>
#include <cassert>
#define repeat(i,n) for (int i = 0; (i) < int(n); ++(i))
#define whole(f,x,...) ([&](decltype((x)) whole) { return (f)(begin(whole), end(whole), ## __VA_ARGS__); })(x)
using ll = long long;
using namespace std;

template <typename M, typename Q>
struct lazy_propagation_segment_tree { // on monoids
int n;
vector<M> a;
vector<Q> q;
function<M (M,M)> append_m; // associative
function<Q (Q,Q)> append_q; // associative, not necessarily commutative
function<M (Q,M)> apply; // distributive, associative
M unit_m; // unit
Q unit_q; // unit
lazy_propagation_segment_tree() = default;
lazy_propagation_segment_tree(int a_n, M a_unit_m, Q a_unit_q, function<M (M,M)> a_append_m, function<Q (Q,Q)> a_append_q, function<M (Q,M)> a_apply) {
n = pow(2,ceil(log2(a_n)));
a.resize(2*n-1, a_unit_m);
q.resize(max(0, 2*n-1-n), a_unit_q);
unit_m = a_unit_m;
unit_q = a_unit_q;
append_m = a_append_m;
append_q = a_append_q;
apply = a_apply;
}
void range_apply(int l, int r, Q z) {
assert (0 <= l and l <= r and r <= n);
range_apply(0, 0, n, l, r, z);
}
void range_apply(int i, int il, int ir, int l, int r, Q z) {
if (l <= il and ir <= r) {
a[i] = apply(z, a[i]);
if (i < q.size()) q[i] = append_q(z, q[i]);
} else if (ir <= l or r <= il) {
// nop
} else {
range_apply(2*i+1, il, (il+ir)/2, 0, n, q[i]);
range_apply(2*i+1, il, (il+ir)/2, l, r, z);
range_apply(2*i+2, (il+ir)/2, ir, 0, n, q[i]);
range_apply(2*i+2, (il+ir)/2, ir, l, r, z);
a[i] = append_m(a[2*i+1], a[2*i+2]);
q[i] = unit_q;
}
}
M range_concat(int l, int r) {
assert (0 <= l and l <= r and r <= n);
return range_concat(0, 0, n, l, r);
}
M range_concat(int i, int il, int ir, int l, int r) {
if (l <= il and ir <= r) {
return a[i];
} else if (ir <= l or r <= il) {
return unit_m;
} else {
return apply(q[i], append_m(
range_concat(2*i+1, il, (il+ir)/2, l, r),
range_concat(2*i+2, (il+ir)/2, ir, l, r)));
}
}
};
template <typename T>
map<T,int> coordinate_compression_map(vector<T> const & xs) {
int n = xs.size();
vector<int> ys(n);
whole(iota, ys, 0);
whole(sort, ys, [&](int i, int j) { return xs[i] < xs[j]; });
map<T,int> f;
for (int i : ys) {
if (not f.count(xs[i])) { // make unique
int j = f.size();
f[xs[i]] = j; // f[xs[i]] has a side effect, increasing the f.size()
}
}
return f;
}

const ll mod = ll(1e18)+9;
struct state_t {
ll size;
array<ll,5> acc;
};
struct query_t {
enum { UNIT, LENGTH, FILL } type;
ll arg1;
int arg2;
bool arg3;
};
int main() {
// input
ll n; int q; cin >> n >> q;
vector<int> x(q); vector<ll> l(q), r(q); repeat (i,q) { cin >> x[i] >> l[i] >> r[i]; ++ r[i]; }
// prepare
map<ll,int> compress; {
vector<ll> ps;
ps.push_back(0);
ps.push_back(n);
repeat (i,q) {
ps.push_back(l[i]);
ps.push_back(r[i]);
}
compress = coordinate_compression_map(ps);
}
lazy_propagation_segment_tree<state_t,query_t> segtree(compress[n], (state_t) { 0, {} }, (query_t) { query_t::UNIT }, [&](state_t const & a, state_t const & b) {
state_t c;
c.size = a.size + b.size;
repeat (i,5) c.acc[i] = a.acc[i] + b.acc[i];
return c;
}, [&](query_t q, query_t p) {
if (q.type == query_t::UNIT) return p;
if (p.type == query_t::UNIT) return q;
assert (q.type == query_t::FILL);
assert (p.type == query_t::FILL);
if (q.arg1 == p.arg1) { // if same color
if (not q.arg3) { // if not reset
q.arg2 += p.arg2;
q.arg3 = p.arg3;
}
} else {
q.arg3 = true; // reset
}
return q;
}, [&](query_t p, state_t a) {
if (p.type == query_t::UNIT) return a;
if (p.type == query_t::LENGTH) return (state_t) { p.arg1, {} };
int color = p.arg1;
int depth = p.arg2;
bool reset = p.arg3;
state_t b = {};
b.size = a.size;
b.acc[color] = ((reset ? 0 : a.acc[color]) + depth * a.size % mod) % mod;
return b;
});
for (auto cur = compress.begin(), nxt = ++ compress.begin(); nxt != compress.end(); ++ cur, ++ nxt) {
assert (cur->second + 1 == nxt->second);
segtree.range_apply(cur->second, nxt->second, (query_t) { query_t::LENGTH, nxt->first - cur->first });
segtree.range_concat(cur->second, nxt->second);
}
// solve
ll acc[5] = {};
repeat (i,q) {
if (x[i] == 0) {
state_t it = segtree.range_concat(compress[l[i]], compress[r[i]]);
int j = whole(max_element, it.acc) - it.acc.begin();
if (whole(count, it.acc, it.acc[j]) == 1) {
acc[j] = (acc[j] + it.acc[j]) % mod;
}
} else {
segtree.range_apply(compress[l[i]], compress[r[i]], (query_t) { query_t::FILL, x[i]-1, 1, false });
}
}
state_t it = segtree.range_concat(compress[0], compress[n]);
repeat (i,5) acc[i] = (acc[i] + it.acc[i]) % mod;
// output
repeat (i,5) cout << acc[i] << ' '; cout << endl;
return 0;
}