#include
#include
#include
using namespace std;
typedef long long ll;
typedef vector> matrix;
typedef vector> d_matrix;
const int maxn = 1e5 + 10;
const int INF = 2e9;
const ll MOD = 998244353;
void print(matrix A) {
int n = (int) A.size(), m = (int) A[0].size();
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
cout << A[i][j] << " ";
}
cout << endl;
}
cout << endl;
}
void print(d_matrix A) {
int n = (int) A.size(), m = (int) A[0].size();
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
cout << A[i][j] << " ";
}
cout << endl;
}
cout << endl;
}
matrix multiply_by_k(matrix A, int k) {
matrix res = A;
int n = (int) A.size(), m = (int) A[0].size();
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
res[i][j] *= k;
}
}
return res;
}
matrix add_two_matrices(matrix A, matrix B) {
int n_a = (int) A.size(), m_a = (int) A[0].size();
int n_b = (int) B.size(), m_b = (int) B[0].size();
if(n_a == n_b and m_a == m_b) {
matrix res = A;
for(int i = 0; i < n_a; i++) {
for(int j = 0; j < m_a; j++) {
res[i][j] = A[i][j] + B[i][j];
}
}
return res;
}
cout << "Dimenziite na matricite treba da se isti za da mozhe da gi sobereme istite" << endl;
return {{0}};
}
matrix subtract_two_matrices(matrix A, matrix B) {
int n_a = (int) A.size(), m_a = (int) A[0].size();
int n_b = (int) B.size(), m_b = (int) B[0].size();
if(n_a != n_b or m_a != m_b) {
cout << "Dimenziite na matricite treba da se isti za da mozhe da gi sobereme istite" << endl;
return {{0}};
}
matrix res = A;
for(int i = 0; i < n_a; i++) {
for(int j = 0; j < m_a; j++) {
res[i][j] = A[i][j] - B[i][j];
}
}
return res;
}
matrix multiply_two_matrices(matrix A, matrix B) {
int n_a = (int) A.size(), m_a = (int) A[0].size();
int n_b = (int) B.size(), m_b = (int) B[0].size();
if(m_a != n_b) {
cout << "Matricite ne mozhat da se mnozhat" << endl;
return {{0}};
}
matrix res(n_a, vector(m_b, 0));
for(int i = 0; i < n_a; i++) {
for(int j = 0; j < m_b; j++) {
int c = 0;
for(int k = 0; k < n_a; k++) {
c += (A[i][k] * B[k][j]) % MOD;
c %= MOD;
}
res[i][j] = c % MOD;
}
}
return res;
}
int determinant_of_matrix(matrix A) {
int sz = (int) A.size();
if(sz == 2) {
return (A[0][0] * A[1][1]) - (A[0][1] * A[1][0]);
}
int determinant = 0;
int sign = 1;
for(int i = 0; i < sz; i++) {
int n = 0, m = 0;
matrix tmp(sz - 1, vector(sz - 1, 0));
for(int j = 0; j < sz; j++) {
for(int k = 0; k < sz; k++) {
if(j != 0 and k != i) {
tmp[n][m] = A[j][k];
if(m < sz - 2) {
m++;
}
else {
m = 0;
n++;
}
}
}
}
determinant = determinant + sign*(A[0][i]) * determinant_of_matrix(tmp);
sign *= -1;
}
return determinant;
}
matrix transpose_matrix(matrix A) {
int n = (int) A.size();
int m = (int) A[0].size();
matrix res(m, vector(n));
for(int j = 0; j < m; j++) {
for(int i = 0; i < n; i++) {
res[j][i] = A[i][j];
}
}
return res;
}
d_matrix inverse_of_matrix(matrix A) {
int n = (int) A.size();
int m = (int) A[0].size();
d_matrix res(n, vector(m));
matrix adj_matrix(n, vector(m));
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
matrix minor(n - 1, vector(m - 1));
int r = 0, c = 0;
for(int a = 0; a < n; a++) {
if(a == i) continue;
for(int b = 0; b < m; b++) {
if(a == i or b == j) continue;
minor[r][c] = A[a][b];
c++;
}
c = 0;
r++;
}
adj_matrix[i][j] = determinant_of_matrix(minor);
if((i + j) % 2 == 1) {
adj_matrix[i][j] *= -1;
}
}
}
adj_matrix = transpose_matrix(adj_matrix);
double det = determinant_of_matrix(A);
cout << det << endl;
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
res[i][j] = (1.0 / det) * adj_matrix[i][j];
}
}
return res;
}
ll power(ll a, ll b) {
ll res = 1;
while(b) {
if(b % 2 == 1) {
res *= a;
}
a *= a;
b /= 2;
}
return res;
}
ll nth_fibbonaci_number(ll x) {
matrix A = {
{1, 1},
{1, 0}
};
matrix B = A;
// for(int i = 0; i < x; i++) {
// A = multiply_two_matrices(A, B);
// }
matrix res = {
{1, 0},
{0, 1}
};
while(x) {
if(x % 2 == 1) {
res = multiply_two_matrices(res, A);
}
A = multiply_two_matrices(A, A);
x /= 2;
}
return res[0][0];
}
int main() {
// nth_fibbonaci_number(8);
// return 0;
for(int i = 1; i <= 10; i++) {
cout << nth_fibbonaci_number(i) << " ";
}
return 0;
}