Fibonacci towers

#pragma GCC optimize("O3,unroll-loops")

#include <bits/stdc++.h>
using namespace std;

#define int long long
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef long double ld;

string to_string(string s) {
    return '"' + s + '"';
}
 
string to_string(const char* s) {
    return to_string((string) s);
}
 
string to_string(bool b) {
    return (b ? "true" : "false");
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A>
string to_string(A v) {
    bool first = true;
    string res = "{";
    for (const auto &x : v) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(x);
    }
    res += "}";
    return res;
}
 
void debug_out() {
    cerr << endl;
}
 
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}
 
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

const int mod = 998244353;

using type = int;

struct Matrix {
    vector <vector <type> > data;

    int row() const { return data.size(); }

    int col() const { return data[0].size(); }

    auto & operator [] (int i) { return data[i]; }

    const auto & operator[] (int i) const { return data[i]; }

    Matrix() = default;

    Matrix(int r, int c): data(r, vector <type> (c)) { }

    Matrix(const vector <vector <type> > &d): data(d) { }

    friend ostream & operator << (ostream &out, const Matrix &d) {
        for (auto x : d.data) {
            for (auto y : x) out << y << ' ';
            out << '\n';
        }
        return out;
    }

    static Matrix identity(long long n) {
        Matrix a = Matrix(n, n);
        while (n--) a[n][n] = 1;
        return a;
    }

    Matrix operator * (const Matrix &b) {
        Matrix a = *this;
        assert(a.col() == b.row());
        Matrix c(a.row(), b.col());
        for (int i = 0; i < a.row(); ++i)
            for (int j = 0; j < b.col(); ++j)
                for (int k = 0; k < a.col(); ++k){
                    c[i][j] += 1ll * a[i][k] % mod * (b[k][j] % mod) % mod;
                    c[i][j] %= mod;
                }
        return c;
    }

    Matrix pow(long long exp) {
        assert(row() == col());
        Matrix base = *this, ans = identity(row());
        for (; exp > 0; exp >>= 1, base = base * base)
            if (exp & 1) ans = ans * base;
        return ans;
    }
};


void solve(){
    int a,b;
    cin>>a>>b;
    // vector<int> dp(b+1);
    // dp[0]=1;
    // for(int i=1;i<=b;i++){
    //     if(i>=a)dp[i]+=dp[i-a];
    //     dp[i]+=dp[i-1];
    //     cerr<<i<<' '<<dp[i]<<'\n';
    // }
    // cout<<dp[b]<<'\n';
    Matrix mat(a, a);
    for (int i=0;i<a;i++){
        // mat[i][i]=1;
        if(i+1<a)mat[i][i+1]=1;
    }
    mat[a-1][a-1]=1;
    mat[a-1][0]=1;
    
    Matrix base(a, 1);
    for (int i=0;i<a;i++){
        base[i][0]=1;
    }

    Matrix ans=mat.pow(b-a+1)*base;

    // cout << mat.pow(b-a) << '\n';
    cout <<ans[a-1][0];
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit); // RTE if input wrong datatype

    int t=1;
    // cin>>t;

    while(t--){
        solve();
    }
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: ACCEPTED

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

Test 41

Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: ACCEPTED

Test 53

Verdict: ACCEPTED

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: ACCEPTED

Test 57

Verdict: ACCEPTED

Test 58

Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

Test 63

Verdict: ACCEPTED

Test 64

Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

Test 66

Verdict: ACCEPTED

Test 67

Verdict: ACCEPTED

Test 68

Verdict: ACCEPTED

Test 69

Verdict: ACCEPTED

Test 70

Verdict: ACCEPTED

Test 71

Verdict: ACCEPTED

Test 72

Verdict: ACCEPTED

Test 73

Verdict: ACCEPTED

Test 74

Verdict: ACCEPTED

Test 75

Verdict: ACCEPTED

Test 76

Verdict: ACCEPTED

Test 77

Verdict: ACCEPTED

Test 78

Verdict: ACCEPTED

Test 79

Verdict: ACCEPTED

Test 80

Verdict: ACCEPTED