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#include "../util.h"
constexpr ll mod = 998244353;
vector<ll> mul(const vector<ll> &a, const vector<ll> &b){
vector<ll> c(sz(a) + sz(b) - 1);
for(int i = 0; i < sz(a); i++){
for(int j = 0; j < sz(b); j++){
c[i+j] += a[i]*b[j] % mod;
}
}
for(ll &x : c) x %= mod;
return c;
}
#include <math/linearRecurrence.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 (sz(cache) <= k) {
ll cur = 0;
for (ll i = 0; i < sz(c); i++) {
cur += (c[i] * cache[sz(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);
for (int j = 0; j < 100; j++) {
ll k = Random::integer<ll>(0, 1000);
ll got = kthTerm(f.f, f.c, k);
ll expected = f(k);
if (got != expected) cerr << "got: " << got << ", expected: " << expected << FAIL;
queries++;
}
}
cerr << "tested random queries: " << queries << endl;
}
constexpr int N = 1'000;
void performance_test() {
timer t;
RandomRecurence f(N);
t.start();
hash_t hash = kthTerm(f.f, f.c, 1e18);
t.stop();
if (t.time > 500) cerr << "too slow: " << t.time << FAIL;
cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl;
}
int main() {
stress_test();
performance_test();
}
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