#include <stdio.h>
#include <stdint.h>

// tiny struct to hold a 2x2 matrix
typedef struct {
    uint64_t m00, m01, m10, m11;
} Matrix2x2;

// multiply two 2x2 matrices together
Matrix2x2 multiply(Matrix2x2 a, Matrix2x2 b) {
    // standard 2x2 matrix multiplication
    return (Matrix2x2) {
        a.m00* b.m00 + a.m01 * b.m10, // top-left
            a.m00* b.m01 + a.m01 * b.m11, // top-right
            a.m10* b.m00 + a.m11 * b.m10, // bottom-left
            a.m10* b.m01 + a.m11 * b.m11  // bottom-right
    };
}

// raise a matrix to the power n using binary exponentiation
Matrix2x2 matrix_pow(Matrix2x2 base, int n) {
    Matrix2x2 result = { 1, 0, 0, 1 }; // start with identity
    while (n > 0) {
        if (n % 2 == 1) result = multiply(result, base); // if odd, multiply once
        base = multiply(base, base); // square the base
        n /= 2; // integer divide n by 2
    }
    return result;
}

// get nth fibonacci number using matrix exponentiation
uint64_t fibonacci_matrix(int n) {
    if (n == 0) return 0; // edge case
    Matrix2x2 base = { 1, 1, 1, 0 }; // Fibonacci Q-matrix
    Matrix2x2 result = matrix_pow(base, n - 1); // raise to (n-1)
    return result.m00; // top-left is F(n)
}

int main() {
    int n = 50; // how many numbers to print
    for (int i = 0; i < n; i++) {
        printf("%llu ", fibonacci_matrix(i)); // print each fib number
    }
    printf("\n"); // newline at end
    return 0;
}
