Fibonacci towers

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

typedef long long ll;
const int MOD = 998244353;

/*
f0 = 1 base
fb = fb-1 + fb-a (b >= a)
fb = fb-1 (1 <= b < a)
*/

vector<vector<ll>> multiply(const vector<vector<ll>> &A, const vector<vector<ll>> &B, int a_size) {
    vector<vector<ll>> C(a_size, vector<ll>(a_size, 0));
    for(int i=0;i<a_size;i++) {
        for(int k=0;k<a_size;k++) {
            if(A[i][k]==0) continue;
            for(int j=0;j<a_size;j++) {
                C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % MOD;
            }
        }
    }
    return C;
}

vector<vector<ll>> matrix_pow(vector<vector<ll>> A, ll power, int a_size) {
    vector<vector<ll>> result(a_size, vector<ll>(a_size, 0));
    for(int i=0;i<a_size;i++) {
        result[i][i] = 1;
    }
    while(power >0){
        if(power &1){
            result = multiply(result, A, a_size);
        }
        A = multiply(A, A, a_size);
        power >>=1;
    }
    return result;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    ll a, b;
    cin >> a >> b;
    if(b < a){
        cout << "1\n";
        return 0;
    }
    int size = a;
    vector<vector<ll>> M(size, vector<ll>(size, 0));
    M[0][0] =1;
    M[0][a-1] =1;
    for(int i=1;i<size;i++) {
        M[i][i-1] =1;
    }
    ll exp = b - (a-1);
    vector<vector<ll>> M_exp = matrix_pow(M, exp, size);
    vector<ll> S(size, 1);
    ll result =0;
    for(int j=0;j<size;j++) {
        result = (result + M_exp[0][j] * S[j]) % MOD;
    }
    cout << result;
}

Test 1

Verdict: ACCEPTED

Test 2

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Test 3

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Test 4

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Test 5

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Test 6

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Test 7

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Test 8

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Test 9

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Test 10

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Test 11

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Test 12

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Test 13

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Test 14

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Test 15

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Test 16

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Test 17

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Test 18

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Test 19

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Test 20

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Test 21

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Test 22

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Test 23

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Test 24

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Test 25

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Test 27

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Test 30

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Test 32

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Test 40

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Test 42

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Test 43

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Test 44

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Test 45

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Test 46

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Test 47

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Test 48

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Test 49

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Test 50

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Test 51

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Test 52

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Test 53

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Test 72

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Test 75

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Test 76

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Test 77

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Test 78

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Test 79

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Test 80

Verdict: ACCEPTED