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#include "../util.h"
constexpr ll mod = 1'394'633'899;
struct mat {
vector<vector<ll>> m;
mat(int dim = 0, int diag = 1) : m(dim, vector<ll>(dim)) {
for (int i = 0; i < dim; i++) m[i][i] = diag;
}
mat(const vector<ll> c) : m(ssize(c), vector<ll>(ssize(c))) {
m[0] = c;
for (ll i = 1; i < ssize(c); i++) {
m[i][i-1] = 1;
}
}
mat operator*(const mat& o) const {
int dim = ssize(m);
mat res(dim, 0);
for (int i = 0; i < dim; i++) {
for (int j = 0; j < dim; j++) {
for (int k = 0; k < dim; k++) {
res.m[i][j] += m[i][k] * o.m[k][j];
res.m[i][j] %= mod;
}
}
}
return res;
}
vector<ll> operator*(const vector<ll>& o) const {
int dim = ssize(m);
vector<ll> res(dim);
for (int i = 0; i < dim; i++) {
for (int j = 0; j < dim; j++) {
res[i] += m[i][j] * o[j];
res[i] %= mod;
}
}
return res;
}
};
#include <math/matrixPower.cpp>
struct RandomRecurence {
vector<ll> f, c, cache;
RandomRecurence(int n) : f(Random::integers<ll>(n, 0, mod)), c(Random::integers<ll>(n, 0, mod)), cache(f) {}
ll operator()(ll k){
while (ssize(cache) <= k) {
ll cur = 0;
for (ll i = 0; i < ssize(c); i++) {
cur += (c[i] * cache[ssize(cache) - i - 1]) % mod;
}
cur %= mod;
cache.push_back(cur);
}
return cache[k];
}
};
void stress_test() {
int queries = 0;
for (int i = 0; i < 10'000; i++) {
int n = Random::integer<int>(1, 10);
RandomRecurence f(n);
precalc(mat(f.c));
auto tmp = f.f;
ranges::reverse(tmp);
for (int j = 0; j < 100; j++) {
ll k = Random::integer<ll>(0, 1000);
vector<ll> got = calc(k, tmp);
vector<ll> expected(ssize(f.f));
for (ll l = 0; l < n; l++) expected[n - 1 - l] = f(k + l);
if (got != expected) cerr << "error" << FAIL;
queries++;
}
}
cerr << "tested random queries: " << queries << endl;
}
constexpr int N = 100;
constexpr int M = 500;
void performance_test() {
timer t;
RandomRecurence f(N);
auto tmp = f.f;
ranges::reverse(tmp);
t.start();
precalc(mat(f.c));
t.stop();
if (t.time > 500) cerr << "too slow precalc: " << t.time << FAIL;
cerr << "tested performance: " << t.time << "ms" << endl;
t.reset();
hash_t hash = 0;
for (int i = 0; i < M; i++) {
ll k = Random::integer<ll>(1e17,1e18);
t.start();
hash += calc(k, tmp).back();
t.stop();
}
if (t.time > 750) cerr << "too slow: " << t.time << FAIL;
cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl;
}
int main() {
stress_test();
if (!sanitize) performance_test();
}
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