问如何在不生成整数的情况下找到第一个k位斐波那契数？

EN

def matrix_mult(a, b):
    return ((a[0][0]*b[0][0] + a[0][1]*b[1][0], 
             a[0][0]*b[0][1] + a[0][1]*b[1][1]),
            (a[1][0]*b[0][0] + a[1][1]*b[1][0], 
             a[1][0]*b[0][1] + a[1][1]*b[1][1]))


def matrix_pow(a, k):
    if k == 0:
        return ((1, 0), (0, 1))
    t = matrix_pow(a, k//2)
    t2 = matrix_mult(t, t)
    if k % 2 == 0:
        return t2
    return matrix_mult(t2, a)


def fib(n):
    a = ((1, 1), (1, 0))
    return matrix_pow(a, n)[0][1]


def get_first_k(n, k):
    return str(fib(n))[:k]

for n in range(10 ** 2, 10 ** 2 + 10):
    print(get_first_k(n, 3))

#output
#first 3 digits   actual number
354               #354224848179261915075
573               #573147844013817084101
927               #927372692193078999176
150               #1500520536206896083277
242               #2427893228399975082453
392               #3928413764606871165730
635               #6356306993006846248183
102               #10284720757613717413913
166               #16641027750620563662096
269               #26925748508234281076009

package stackoverflow;

import java.math.BigInteger;

public class Fibonacci {

    public static class Matrix {
        BigInteger[][] a;

        public Matrix(BigInteger n0, BigInteger n1, BigInteger n2, BigInteger n3) {
            a = new BigInteger[][]{{n0, n1}, {n2, n3}};
        }

        public BigInteger get(int i, int j) {
            return a[i][j];
        }

        @Override
        public String toString() {
            return String.format("%s %s\n%s %s", a[0][0], a[0][1], a[1][0], a[1][1]);
        }
    }

    Matrix matrixMult(Matrix a, Matrix b) {
        return new Matrix(a.get(0, 0).multiply(b.get(0, 0)).add(a.get(0, 1).multiply(b.get(1, 0))),
                          a.get(0, 0).multiply(b.get(0, 1)).add(a.get(0, 1).multiply(b.get(1, 1))),
                          a.get(1, 0).multiply(b.get(0, 0)).add(a.get(1, 1).multiply(b.get(1, 0))),
                          a.get(1, 0).multiply(b.get(0, 1)).add(a.get(1, 1).multiply(b.get(1, 1))));
    }

    Matrix power(Matrix a, int k) {
        if (k == 0)
            return new Matrix(new BigInteger("1"), new BigInteger("0"),
                              new BigInteger("0"), new BigInteger("1"));
        Matrix t = power(a, k / 2);
        Matrix t2 = matrixMult(t, t);
        if (k % 2 == 0)
            return t2;
        return matrixMult(t2, a);
    }

    BigInteger get(int n) {
        Matrix a = new Matrix(new BigInteger("1"), new BigInteger("1"),
                              new BigInteger("1"), new BigInteger("0"));
        return power(a, n).get(0, 1);
    }

    String getFirstK(int n, int k) {
        return get(n).toString().substring(0, k);
    }

    public static void main(String[] args) {
        Fibonacci f = new Fibonacci();

        System.out.println(f.getFirstK(200000, 10));
    }
}